Problem 45831. Compute the Bernoulli numbers
The Bernoulli numbers appear in several applications in number theory, including expressions for sums of powers and certain values of the Riemann zeta function. For each index m, the Bernoulli numbers have two values, one denoted with a plus superscript and one denoted with a minus superscript.
For m = 0, 1, 2, 3, 4, the "plus" values are = 1, 1/2, 1/6, 0, and -1/30, respectively. The "minus" values are the same, except for m = 1, for which the value is -1/2.
Compute the two values of the Bernoulli numbers for the given index. Round to seven places after the decimal.
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