MartinMikkelsen

Hi, is this what you are looking for? [Documentation, Mathematical functions](https://mpmath.org/doc/current/functions/index.html)

Hi, seems to be a typo in your script. I cannot reproduce the same results. ``` from mpmath import * mp.pretty = True mp.dps = 15 y = [-1, -4,...

For future reference, I have implemented the method from this [article](https://articles.adsabs.harvard.edu/pdf/1993ApJS...84..101A). [This](https://github.com/MartinMikkelsen/FewSpecialFunctions.jl/blob/main/src/FermiDirac.jl) contains Fermi-Dirac integrals of orders -1/2, 1/2, 3/2, and 5/2 over the entire range to high precision.

Have you looked into [Cauchy principal value](https://en.wikipedia.org/wiki/Cauchy_principal_value)?

I've also calculated the Cauchy principal value but unfortunately didn't have time to post it. I followed a similar approach to you @stevengj and got `0.159706`.