{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-06T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":58394,"title":"Integrate a product of gamma functions","description":"Write a function to compute the following integral:\r\n\r\nwhere  and  is the gamma function, the subject of Cody Problem 46025.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 104.1px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52.05px; transform-origin: 407px 52.05px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 152.742px 8px; transform-origin: 152.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the following integral:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 196.5px; height: 44px;\" width=\"196.5\" height=\"44\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.1px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.55px; text-align: left; transform-origin: 384px 10.55px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 56px; height: 20px;\" width=\"56\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 29.5px; height: 18.5px;\" width=\"29.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 117.842px 8px; transform-origin: 117.842px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the gamma function, the subject of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46025\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 46025\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = intGammaProduct(a)\r\n  f = @(x) gamma(1+i*a*x)*gamma(1-i*a*x);\r\n  y = trapz(x,f);\r\nend","test_suite":"%%\r\na = tan(1);\r\nI_correct = 1.008596722571773;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)\r\n\r\n%%\r\na = sqrt(2);\r\nI_correct = 1.110720734539592;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)\r\n\r\n%%\r\na = log(3);\r\nI_correct = 1.429800433690064;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)\r\n\r\n%%\r\na = exp(4);\r\nI_correct = 0.028770138289325;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)\r\n\r\n%%\r\na = sinh(5);\r\nI_correct = 0.021168845856719;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)\r\n\r\n%%\r\na = asinh(6);\r\nI_correct = 0.630391294450658;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-06-03T19:50:53.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-06-03T14:18:04.000Z","updated_at":"2026-01-26T04:29:04.000Z","published_at":"2023-06-03T14:18:04.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the following integral:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI = \\\\int_{-\\\\infty}^\\\\infty \\\\Gamma(1+iax)\\\\Gamma(1-iax) dx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei = \\\\sqrt{-1}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Gamma(z)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the gamma function, the subject of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/46025\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 46025\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59571,"title":"Compute a sum involving the zeta function","description":"Write a function to compute the sum\r\n\r\nfor , where  is the zeta function, the subject of Cody Problems 45939, 45988, and 45997.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 105px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52.5px; transform-origin: 407px 52.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 111.883px 8px; transform-origin: 111.883px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the sum\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"137.5\" height=\"45\" alt=\"S(x) = sum(zeta(n+1) x^n) for n = 1 to n = inf\" style=\"width: 137.5px; height: 45px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.1083px 8px; transform-origin: 10.1083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003efor \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46.5\" height=\"18.5\" alt=\"|x| \u003c 1\" style=\"width: 46.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.8917px 8px; transform-origin: 24.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEQAAAAlCAYAAAD7u09NAAAEdklEQVRoQ+2ZS6hPURTG3TkRIwYUBpRXeZZMDCgpSXlEuiOPgQxEMTAwoOgOZOCRgYwwkZQiMRB5TJBigDJh5FHM+X63s7Tvtl/nnHsu6pz6uqf/3mudvb/13PsOjOufEQwM9HyMZKAnxPOInpB/gJClWsNM4WrH4TpL+pfU/c5YewhknBHWCV86JgT1J4UZwpbSb9UhZI+UbhTWlir35kHGZWHlGJFhnzdPLCKlhJDJ0vxQeCkcEd5VX4Kg/cIcYa9wLkEUOj4Im4Q7DQltI/ZYwpcyaxzWX0IIDG8WZldkmKUhgueHsFp4llgxC4KQIiu12XlEljXfExZVe4h+ooSQ25JeI+AFPKeE8dX7G/3FS1JWRxYdRmgH+y1SiWHJJytSs0sIgd0bwtRKER7xSLguXBNyyfFve4ft3wyzTD9EvbmEEBQaKcf0nsoVPvnIPRW2Cl2X2RI3+ahJD4Ro6JYQYmQMZkIjtKDz+nGXMKXAk0o21HYORqHkT4gpyhFCdXgl0DucaLCa15XM3AayXYgcltLjQjRscoSQDL+lXCyz6p8afyKkEhmk01EuFqgCJL6JgvUrxP5pgapG/nIrhTV6y/X7J2FexhMtj0TbhBQh9BlHhVWC9R51rGb5g6p0KCFohBzQHBbMc0HYLdgabuqd0PPH0H1LoC1wx2KfM0Kia4oRYo0U7tUkVFhQ9uPeqtn82eo3umHOO5T09QIGwdt4aA6/VmM79ZeKYWM58pFnLtUxmFhjhHAG2CHkXDBmiSaEWAImLA56ZBi56MXdXaLcMYjMdcLJMI4R8l2K23hHE0JIwOQJcs50wQ1VS4bkCZ5BZ+MYDwJLcoh5SDSvhQjBla4IyQYm5RrVWJ2QIUQ/V3LmIW6/Y90yUyy/2BJo/EiqeEbu4Gnf8XX83k6IEGr1AqHtqZT7iLdCSVy7+YONbRPcDhiP5bgQ8gI3t+TyXdZIIUJgnLI3Gr1DSdnFOnaA5N33TDdHkFDdTbtjJR5t86Odc4gQNoElphWERW4K5JIPcrrMA4ht//LIcgShRI/ieo6Nccgs8WibHz1oxghhoyUZO0eIJcNU657yAPRbsg3lCMsfVkYJvfdCrNKQi+anDBQihAOQnWxR/EKg7t8VUnceIXIsj6QukKzcIu9bzuQZC+mw/MEYRHD4TF1PMj+Z00KEmFvFrB9KeilPwYo8sfbdLbf+HDfZ+mRZJ4xuQo1nuxDrqk1X8l4m15iZp/gbzp1P3PmpCyLXA/yEiQ4rt6EcgexzgepDyLjXmyEDYRi8nSNB9Mkd7hDEEjyEi3tZVOdIT1gsFJK3VamFthyjt7oo+En5D7UlhPhCTdp6u6jm1FrngqklD8PitS64mxBCzzBJyHWF/mbsbmVD5W2jsdkSHcU37ijLEWIVwFpdyiixmrtljy0UUjiu7xsjUjDe/TpemSPEypq7wVDyK7GUzbH7j9yptI7O0FySLt+q1SrkCKFU2b8d2MCQ0PVG2hLRSj5HSCvl/6NwT4hntZ6QnpB0IP8C3IMRNWT+n34AAAAASUVORK5CYII=\" width=\"34\" height=\"18.5\" alt=\"zeta(m)\" style=\"width: 34px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.517px 8px; transform-origin: 157.517px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the zeta function, the subject of Cody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45939\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e45939\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45988\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e45988\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45997\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e45997\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function S = zetasum(x)\r\n  n = 1:Inf;\r\n  S = sum(zeta(n+1).*x.^n);\r\nend","test_suite":"%%\r\nx = 1/2;\r\nS = zetasum(x);\r\nS_correct = 1.386294361119891;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 2/3;\r\nS = zetasum(x);\r\nS_correct = 2.554818115119273;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 3/4;\r\nS = zetasum(x);\r\nS_correct = 3.650237868474732;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 5/6;\r\nS = zetasum(x);\r\nS_correct = 5.754911840473381;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 7/8;\r\nS = zetasum(x);\r\nS_correct = 7.811276998394322;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 8/9;\r\nS = zetasum(x);\r\nS_correct = 8.83072761223029;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 9/10;\r\nS = zetasum(x);\r\nS_correct = 9.84653927550954;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 10/11;\r\nS = zetasum(x);\r\nS_correct = 10.85964675709217;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 11/12;\r\nS = zetasum(x);\r\nS_correct = 11.87068966352595;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%% \r\nx = 0.232931374143;\r\nSS = zetasum(zetasum(x));\r\nSS_correct = 1.227707484938568;\r\nassert(abs(SS-SS_correct)/SS_correct\u003c1e-12)\r\n\r\n%%\r\nx = 1./primes(20);\r\ny = sum(arrayfun(@zetasum,x));\r\ny_correct = 3.2640541637441439;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\nfiletext = fileread('zetasum.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp') || contains(filetext,'switch'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2024-01-20T17:57:17.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-01-20T13:37:10.000Z","updated_at":"2026-03-04T13:56:18.000Z","published_at":"2024-01-20T13:40:38.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the sum\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S(x) = sum(zeta(n+1) x^n) for n = 1 to n = inf\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS(x) = \\\\sum_{n=1}^\\\\infty \\\\zeta(n+1) x^n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003efor \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"|x| \u0026lt; 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e|x| \u0026lt; 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"zeta(m)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\zeta(m)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the zeta function, the subject of Cody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45939\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e45939\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45988\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e45988\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45997\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e45997\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59521,"title":"Integrate a power tower","description":"Write a function to compute this integral\r\n\r\nwhere . That is, the integrand is (x to the x) to the (x to the x) to the (x to the x)...","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 104px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52px; transform-origin: 407px 52px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 122.783px 8px; transform-origin: 122.783px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute this integral\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"135\" height=\"44\" alt=\"I = integral((x^x)^(x^x)^(x^x)...,{x,a,0})\" style=\"width: 135px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAH4AAAAkCAYAAABPNo4ZAAAEKklEQVR4Xu1aO8wOQRT9/54QKgoKCn+CKLxCpyARyR8NIioSj1I8gqgUCIWI5PcoFKLwKDQiodV4VEJCQUFBhQg958jcuBmzO7szs7vfl5lNTjb5dnfm3nPuvfP6JifKlSUDk1l6XZyeKMJnGgRF+CJ8pgxk6nbJ+CJ8pgxk6rYv45eAl7PAYsPPItxfA6eBl5lyNqpui1ZzYeAWn5F1wh/Ex1eB58BW4Jtp7C7uO4AbwAFfBx08n6ds6aD5QZqM8UkEpya8nsQIvxkfPwZ+AauAD4oOGvkGWACcAs71RJV2cC36HPeKQx5PAIcAVtUQHk8afZjl1Cxa+M9G2Hu473QIyw5pLAODw4BUgy5iwI7oL+hkeoyF14LPMhwew/1aAHnkRpLyd6zwUuLZDqPRZdAa/P7CdHQR9+MBRvs+cQl+Gx+d7zjQfHaFPncJ/giNsWrqihrafrTwLPFSNupKqnT0Du9PhVrr+K4IHkZmtPDSAMv47BobnuHZOvN8foIsZLDtA2SSwpI+zhnOAGYl3A1ISU+Z4bY0UcLT2PemxTbCc/nA2WTIRcHPqCDqQ3CpKivR7w9j9CXc9wIbAK5mQocvu2KRxy4FF86jhJfZPBtrI3zI7H4IwenXBYCTKU5cZXzVKxW+ExLIQwmeXHiu39fXpPB1PNtvnrcRfijBaarsQVB0Tlz1akSGLlac5dazuko2tODJhfdtBEjmsOM2wnN5yLLKfQBeJPqwEaWO4NhnIrq9ISXtivA+v207uMK5Ash8h5UyZqgI9XNsSj0DgIILYV0GgOw7kNSqlYoQV7WE9QnCADgKyOS07wCIEp5j3VfjYZsxPmRMFCJdpT9lBaBPHwHOrKuymUF4xxi0FPeYdbWr9PdRAaKEp+8/DUlNhed7m4DYLdSuAkAPSVXZLmWeexIbgRQ7kX0HQLTwegOnLvolQFiiF/rqYIvndgDElkzZfq4SVa9kqraoW5j/36t2APAF1+Qypg9+Gy283rLdhQY5KbIvvd7v6pQuRcZoO6tEfQvnlhkHq/yNFYXf21u2qQMgWnga1OaQxj69S0GSbsMVAE371NnsClAGNQ+ZZILJCvcd4HFzyGlZE99dAZAi4JIIrwlzbcdKYLRZxjUhpe6dkGNZnfH2xE5XMs7EORRsAx4Cl4GQ07I2PqY4ltX9JRGeDUrJtw9hhv4jBsUkaU0nk/pMgeK/AvYATwEu3bidKhlPX291mO2uwKAvq4HQLW+2qRO10aGZ769XbPAIsAL4BMwx9wc9ZESb7PFVihlDDt8jwTcByXhZ45OwPjI9lV+SnNuVb9K2nHfcr0oQn/ApjSxtjRADQwivS28oFaP01yu9TxDqT59zpb82FuFDpfr3XRE+nsPSQl8MDJHxfflW+qlhoAifaXgU4YvwmTKQqdsl4zMV/g/oTTM0yd5g8QAAAABJRU5ErkJggg==\" width=\"63\" height=\"18\" style=\"width: 63px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 226.3px 8px; transform-origin: 226.3px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. That is, the integrand is (x to the x) to the (x to the x) to the (x to the x)...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function I = intPowerTower(a)\r\n  I = integral(x^x^x^x^x^x^x^x,0,a);\r\nend","test_suite":"%%\r\na = 0;\r\nI = intPowerTower(a);\r\nassert(abs(I)\u003c1e-6)\r\n\r\n%%\r\na = 1/100;\r\nI = intPowerTower(a);\r\nI_correct = 0.00975627404012066;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1/20;\r\nI = intPowerTower(a);\r\nI_correct = 0.04621245261821598;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1/10;\r\nI = intPowerTower(a);\r\nI_correct = 0.0886781687569094;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1/5;\r\nI = intPowerTower(a);\r\nI_correct = 0.1685639964895788;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1/4;\r\nI = intPowerTower(a);\r\nI_correct = 0.2071658901263798;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 3/8;\r\nI = intPowerTower(a);\r\nI_correct = 0.30215124860335973;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1/2;\r\nI = intPowerTower(a);\r\nI_correct = 0.3972053202401857;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 2/3;\r\nI = intPowerTower(a);\r\nI_correct = 0.5277402852630483;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 3/4;\r\nI = intPowerTower(a);\r\nI_correct = 0.5959989560650945;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 5/6;\r\nI = intPowerTower(a);\r\nI_correct = 0.6671963910854818;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1;\r\nI = intPowerTower(a);\r\nI_correct = 0.822467033424113;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = (rand+3)/4;\r\nI = intPowerTower(a);\r\nI_correct = polyval([0.3875275 -0.9886411 1.132527 0.1505356 0.1405179],a);\r\nassert(abs(I-I_correct)\u003c5e-6)\r\n\r\n%%\r\nfiletext = fileread('intPowerTower.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp') || contains(filetext,'find') || contains(filetext,'switch'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":46909,"edited_by":46909,"edited_at":"2024-01-03T15:06:22.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-12-31T18:50:11.000Z","updated_at":"2026-01-28T06:58:04.000Z","published_at":"2023-12-31T18:50:21.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute this integral\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"I = integral((x^x)^(x^x)^(x^x)...,{x,a,0})\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI = \\\\int_0^a {(x^x)^{(x^x)^{(x^x)\\\\ldots}} dx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 \\\\le a \\\\le 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. That is, the integrand is (x to the x) to the (x to the x) to the (x to the x)...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":58394,"title":"Integrate a product of gamma functions","description":"Write a function to compute the following integral:\r\n\r\nwhere  and  is the gamma function, the subject of Cody Problem 46025.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 104.1px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52.05px; transform-origin: 407px 52.05px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 152.742px 8px; transform-origin: 152.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the following integral:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 196.5px; height: 44px;\" width=\"196.5\" height=\"44\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.1px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.55px; text-align: left; transform-origin: 384px 10.55px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 56px; height: 20px;\" width=\"56\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 29.5px; height: 18.5px;\" width=\"29.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 117.842px 8px; transform-origin: 117.842px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the gamma function, the subject of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46025\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 46025\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = intGammaProduct(a)\r\n  f = @(x) gamma(1+i*a*x)*gamma(1-i*a*x);\r\n  y = trapz(x,f);\r\nend","test_suite":"%%\r\na = tan(1);\r\nI_correct = 1.008596722571773;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)\r\n\r\n%%\r\na = sqrt(2);\r\nI_correct = 1.110720734539592;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)\r\n\r\n%%\r\na = log(3);\r\nI_correct = 1.429800433690064;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)\r\n\r\n%%\r\na = exp(4);\r\nI_correct = 0.028770138289325;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)\r\n\r\n%%\r\na = sinh(5);\r\nI_correct = 0.021168845856719;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)\r\n\r\n%%\r\na = asinh(6);\r\nI_correct = 0.630391294450658;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-06-03T19:50:53.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-06-03T14:18:04.000Z","updated_at":"2026-01-26T04:29:04.000Z","published_at":"2023-06-03T14:18:04.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the following integral:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI = \\\\int_{-\\\\infty}^\\\\infty \\\\Gamma(1+iax)\\\\Gamma(1-iax) dx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei = \\\\sqrt{-1}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Gamma(z)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the gamma function, the subject of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/46025\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 46025\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59571,"title":"Compute a sum involving the zeta function","description":"Write a function to compute the sum\r\n\r\nfor , where  is the zeta function, the subject of Cody Problems 45939, 45988, and 45997.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 105px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52.5px; transform-origin: 407px 52.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 111.883px 8px; transform-origin: 111.883px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the sum\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"137.5\" height=\"45\" alt=\"S(x) = sum(zeta(n+1) x^n) for n = 1 to n = inf\" style=\"width: 137.5px; height: 45px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.1083px 8px; transform-origin: 10.1083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003efor \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46.5\" height=\"18.5\" alt=\"|x| \u003c 1\" style=\"width: 46.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.8917px 8px; transform-origin: 24.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"34\" height=\"18.5\" alt=\"zeta(m)\" style=\"width: 34px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.517px 8px; transform-origin: 157.517px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the zeta function, the subject of Cody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45939\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e45939\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45988\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e45988\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45997\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e45997\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function S = zetasum(x)\r\n  n = 1:Inf;\r\n  S = sum(zeta(n+1).*x.^n);\r\nend","test_suite":"%%\r\nx = 1/2;\r\nS = zetasum(x);\r\nS_correct = 1.386294361119891;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 2/3;\r\nS = zetasum(x);\r\nS_correct = 2.554818115119273;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 3/4;\r\nS = zetasum(x);\r\nS_correct = 3.650237868474732;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 5/6;\r\nS = zetasum(x);\r\nS_correct = 5.754911840473381;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 7/8;\r\nS = zetasum(x);\r\nS_correct = 7.811276998394322;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 8/9;\r\nS = zetasum(x);\r\nS_correct = 8.83072761223029;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 9/10;\r\nS = zetasum(x);\r\nS_correct = 9.84653927550954;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 10/11;\r\nS = zetasum(x);\r\nS_correct = 10.85964675709217;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 11/12;\r\nS = zetasum(x);\r\nS_correct = 11.87068966352595;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%% \r\nx = 0.232931374143;\r\nSS = zetasum(zetasum(x));\r\nSS_correct = 1.227707484938568;\r\nassert(abs(SS-SS_correct)/SS_correct\u003c1e-12)\r\n\r\n%%\r\nx = 1./primes(20);\r\ny = sum(arrayfun(@zetasum,x));\r\ny_correct = 3.2640541637441439;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\nfiletext = fileread('zetasum.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp') || contains(filetext,'switch'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2024-01-20T17:57:17.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-01-20T13:37:10.000Z","updated_at":"2026-03-04T13:56:18.000Z","published_at":"2024-01-20T13:40:38.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the sum\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S(x) = sum(zeta(n+1) x^n) for n = 1 to n = inf\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS(x) = \\\\sum_{n=1}^\\\\infty \\\\zeta(n+1) x^n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003efor \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"|x| \u0026lt; 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e|x| \u0026lt; 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"zeta(m)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\zeta(m)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the zeta function, the subject of Cody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45939\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e45939\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45988\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e45988\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45997\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e45997\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59521,"title":"Integrate a power tower","description":"Write a function to compute this integral\r\n\r\nwhere . That is, the integrand is (x to the x) to the (x to the x) to the (x to the x)...","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 104px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52px; transform-origin: 407px 52px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 122.783px 8px; transform-origin: 122.783px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute this integral\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"135\" height=\"44\" alt=\"I = integral((x^x)^(x^x)^(x^x)...,{x,a,0})\" style=\"width: 135px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAH4AAAAkCAYAAABPNo4ZAAAEKklEQVR4Xu1aO8wOQRT9/54QKgoKCn+CKLxCpyARyR8NIioSj1I8gqgUCIWI5PcoFKLwKDQiodV4VEJCQUFBhQg958jcuBmzO7szs7vfl5lNTjb5dnfm3nPuvfP6JifKlSUDk1l6XZyeKMJnGgRF+CJ8pgxk6nbJ+CJ8pgxk6rYv45eAl7PAYsPPItxfA6eBl5lyNqpui1ZzYeAWn5F1wh/Ex1eB58BW4Jtp7C7uO4AbwAFfBx08n6ds6aD5QZqM8UkEpya8nsQIvxkfPwZ+AauAD4oOGvkGWACcAs71RJV2cC36HPeKQx5PAIcAVtUQHk8afZjl1Cxa+M9G2Hu473QIyw5pLAODw4BUgy5iwI7oL+hkeoyF14LPMhwew/1aAHnkRpLyd6zwUuLZDqPRZdAa/P7CdHQR9+MBRvs+cQl+Gx+d7zjQfHaFPncJ/giNsWrqihrafrTwLPFSNupKqnT0Du9PhVrr+K4IHkZmtPDSAMv47BobnuHZOvN8foIsZLDtA2SSwpI+zhnOAGYl3A1ISU+Z4bY0UcLT2PemxTbCc/nA2WTIRcHPqCDqQ3CpKivR7w9j9CXc9wIbAK5mQocvu2KRxy4FF86jhJfZPBtrI3zI7H4IwenXBYCTKU5cZXzVKxW+ExLIQwmeXHiu39fXpPB1PNtvnrcRfijBaarsQVB0Tlz1akSGLlac5dazuko2tODJhfdtBEjmsOM2wnN5yLLKfQBeJPqwEaWO4NhnIrq9ISXtivA+v207uMK5Ash8h5UyZqgI9XNsSj0DgIILYV0GgOw7kNSqlYoQV7WE9QnCADgKyOS07wCIEp5j3VfjYZsxPmRMFCJdpT9lBaBPHwHOrKuymUF4xxi0FPeYdbWr9PdRAaKEp+8/DUlNhed7m4DYLdSuAkAPSVXZLmWeexIbgRQ7kX0HQLTwegOnLvolQFiiF/rqYIvndgDElkzZfq4SVa9kqraoW5j/36t2APAF1+Qypg9+Gy283rLdhQY5KbIvvd7v6pQuRcZoO6tEfQvnlhkHq/yNFYXf21u2qQMgWnga1OaQxj69S0GSbsMVAE371NnsClAGNQ+ZZILJCvcd4HFzyGlZE99dAZAi4JIIrwlzbcdKYLRZxjUhpe6dkGNZnfH2xE5XMs7EORRsAx4Cl4GQ07I2PqY4ltX9JRGeDUrJtw9hhv4jBsUkaU0nk/pMgeK/AvYATwEu3bidKhlPX291mO2uwKAvq4HQLW+2qRO10aGZ769XbPAIsAL4BMwx9wc9ZESb7PFVihlDDt8jwTcByXhZ45OwPjI9lV+SnNuVb9K2nHfcr0oQn/ApjSxtjRADQwivS28oFaP01yu9TxDqT59zpb82FuFDpfr3XRE+nsPSQl8MDJHxfflW+qlhoAifaXgU4YvwmTKQqdsl4zMV/g/oTTM0yd5g8QAAAABJRU5ErkJggg==\" width=\"63\" height=\"18\" style=\"width: 63px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 226.3px 8px; transform-origin: 226.3px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. That is, the integrand is (x to the x) to the (x to the x) to the (x to the x)...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function I = intPowerTower(a)\r\n  I = integral(x^x^x^x^x^x^x^x,0,a);\r\nend","test_suite":"%%\r\na = 0;\r\nI = intPowerTower(a);\r\nassert(abs(I)\u003c1e-6)\r\n\r\n%%\r\na = 1/100;\r\nI = intPowerTower(a);\r\nI_correct = 0.00975627404012066;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1/20;\r\nI = intPowerTower(a);\r\nI_correct = 0.04621245261821598;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1/10;\r\nI = intPowerTower(a);\r\nI_correct = 0.0886781687569094;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1/5;\r\nI = intPowerTower(a);\r\nI_correct = 0.1685639964895788;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1/4;\r\nI = intPowerTower(a);\r\nI_correct = 0.2071658901263798;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 3/8;\r\nI = intPowerTower(a);\r\nI_correct = 0.30215124860335973;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1/2;\r\nI = intPowerTower(a);\r\nI_correct = 0.3972053202401857;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 2/3;\r\nI = intPowerTower(a);\r\nI_correct = 0.5277402852630483;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 3/4;\r\nI = intPowerTower(a);\r\nI_correct = 0.5959989560650945;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 5/6;\r\nI = intPowerTower(a);\r\nI_correct = 0.6671963910854818;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1;\r\nI = intPowerTower(a);\r\nI_correct = 0.822467033424113;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = (rand+3)/4;\r\nI = intPowerTower(a);\r\nI_correct = polyval([0.3875275 -0.9886411 1.132527 0.1505356 0.1405179],a);\r\nassert(abs(I-I_correct)\u003c5e-6)\r\n\r\n%%\r\nfiletext = fileread('intPowerTower.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp') || contains(filetext,'find') || contains(filetext,'switch'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":46909,"edited_by":46909,"edited_at":"2024-01-03T15:06:22.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-12-31T18:50:11.000Z","updated_at":"2026-01-28T06:58:04.000Z","published_at":"2023-12-31T18:50:21.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute this integral\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"I = integral((x^x)^(x^x)^(x^x)...,{x,a,0})\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI = \\\\int_0^a {(x^x)^{(x^x)^{(x^x)\\\\ldots}} dx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 \\\\le a \\\\le 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. That is, the integrand is (x to the x) to the (x to the x) to the (x to the x)...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"term":"tag:\"maths 505\"","current_player_id":null,"fields":[{"name":"page","type":"integer","callback":null,"default":1,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"per_page","type":"integer","callback":null,"default":50,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"sort","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"body","type":"text","callback":null,"default":"*:*","directive":null,"facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":false},{"name":"group","type":"string","callback":null,"default":null,"directive":"group","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"difficulty_rating_bin","type":"string","callback":null,"default":null,"directive":"difficulty_rating_bin","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"id","type":"integer","callback":null,"default":null,"directive":"id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"tag","type":"string","callback":null,"default":null,"directive":"tag","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"product","type":"string","callback":null,"default":null,"directive":"product","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_at","type":"timeframe","callback":{},"default":null,"directive":"created_at","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"profile_id","type":"integer","callback":null,"default":null,"directive":"author_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_by","type":"string","callback":null,"default":null,"directive":"author","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player_id","type":"integer","callback":null,"default":null,"directive":"solver_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player","type":"string","callback":null,"default":null,"directive":"solver","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"solvers_count","type":"integer","callback":null,"default":null,"directive":"solvers_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"comments_count","type":"integer","callback":null,"default":null,"directive":"comments_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"likes_count","type":"integer","callback":null,"default":null,"directive":"likes_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leader_id","type":"integer","callback":null,"default":null,"directive":"leader_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leading_solution","type":"integer","callback":null,"default":null,"directive":"leading_solution","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true}],"filters":[{"name":"asset_type","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":"\"cody:problem\"","prepend":true},{"name":"profile_id","type":"integer","callback":{},"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":"author_id","static":null,"prepend":true}],"query":{"params":{"per_page":50,"term":"tag:\"maths 505\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"maths 505\"","","\"","maths 505","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007fdd454b0788\u003e":null,"#\u003cMathWorks::Search::Field:0x00007fdd454b06e8\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007fdd2f6bfdc8\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007fdd454b0a08\u003e":1,"#\u003cMathWorks::Search::Field:0x00007fdd454b0968\u003e":50,"#\u003cMathWorks::Search::Field:0x00007fdd454b08c8\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007fdd454b0828\u003e":"tag:\"maths 505\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007fdd454b0828\u003e":"tag:\"maths 505\""},"queried_facets":{}},"query_backend":{"connection":{"configuration":{"index_url":"http://index-op-v2/solr/","query_url":"http://search-op-v2/solr/","direct_access_index_urls":["http://index-op-v2/solr/"],"direct_access_query_urls":["http://search-op-v2/solr/"],"timeout":10,"vhost":"search","exchange":"search.topic","heartbeat":30,"pre_index_mode":false,"host":"rabbitmq-eks","port":5672,"username":"cody-search","password":"78X075ddcV44","virtual_host":"search","indexer":"amqp","http_logging":"true","core":"cody"},"query_connection":{"uri":"http://search-op-v2/solr/cody/","proxy":null,"connection":{"parallel_manager":null,"headers":{"User-Agent":"Faraday v1.0.1"},"params":{},"options":{"params_encoder":"Faraday::FlatParamsEncoder","proxy":null,"bind":null,"timeout":null,"open_timeout":null,"read_timeout":null,"write_timeout":null,"boundary":null,"oauth":null,"context":null,"on_data":null},"ssl":{"verify":true,"ca_file":null,"ca_path":null,"verify_mode":null,"cert_store":null,"client_cert":null,"client_key":null,"certificate":null,"private_key":null,"verify_depth":null,"version":null,"min_version":null,"max_version":null},"default_parallel_manager":null,"builder":{"adapter":{"name":"Faraday::Adapter::NetHttp","args":[],"block":null},"handlers":[{"name":"Faraday::Response::RaiseError","args":[],"block":null}],"app":{"app":{"ssl_cert_store":{"verify_callback":null,"error":null,"error_string":null,"chain":null,"time":null},"app":{},"connection_options":{},"config_block":null}}},"url_prefix":"http://search-op-v2/solr/cody/","manual_proxy":false,"proxy":null},"update_format":"RSolr::JSON::Generator","update_path":"update","options":{"url":"http://search-op-v2/solr/cody"}}},"query":{"params":{"per_page":50,"term":"tag:\"maths 505\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"maths 505\"","","\"","maths 505","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007fdd454b0788\u003e":null,"#\u003cMathWorks::Search::Field:0x00007fdd454b06e8\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007fdd2f6bfdc8\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007fdd454b0a08\u003e":1,"#\u003cMathWorks::Search::Field:0x00007fdd454b0968\u003e":50,"#\u003cMathWorks::Search::Field:0x00007fdd454b08c8\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007fdd454b0828\u003e":"tag:\"maths 505\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007fdd454b0828\u003e":"tag:\"maths 505\""},"queried_facets":{}},"options":{"fields":["id","difficulty_rating"]},"join":" "},"results":[{"id":58394,"difficulty_rating":"medium"},{"id":59571,"difficulty_rating":"medium"},{"id":59521,"difficulty_rating":"medium-hard"}]}}