Does MATLAB have inverse tangent integral TI2(z)?

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HC98
HC98 on 3 Oct 2022
Edited: Torsten on 3 Oct 2022
In Mathematica, one calls the function using :
(PolyLog[2, I z] - PolyLog[2, -I z])/(2 I)
How dl I implement this in matlab, is there a built in function for the tangent integral?

Answers (2)

Star Strider
Star Strider on 3 Oct 2022
The polylog function exists in the Symbolic Math Toolbox. It supports symbolic and numeric (double) arguments.

Torsten
Torsten on 3 Oct 2022
Edited: Torsten on 3 Oct 2022
format long
x = 0.5;
Ti2 = 1i*( -dilog(1-1i*x) + 0.25*dilog(1+x.^2) )
Ti2 =
0.487222358294522
Ti2_compare = integral(@(x)atan(x)./x,0,x)
Ti2_compare =
0.487222358294522

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