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I am looking for a reliable library where I can find polylogarithm function and newton/secant method for solving non-linear equations. Basically I have something like this:

f(x) = x - A*PolyLog(3/2, B*Exp(-t*x))
f(x) = 0

and 

f(x,y,z) = 0
g(x,y,z) = 0
h(x,y,z) = 0

involving polylogarithm function. Implementation of Polylogarithm function need to be similar to that of Mathematica or Python (can return complex values) and defined for non-integer value (here we have 3/2). So, Newton method should also work for complex numbers.

The library should be written in Fortran or C/C++.

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One way to implement Polylogarithm functions can be found in the book "Numerical Recipes: The Art of Scientific Computing". The book includes some of the theory and practical aspects of evaluating special functions and finding zeros of equations. If you want, you can also buy the codes at their web page.

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  • $\begingroup$ What you are providing in this answer is what is well known about the book you are suggesting. Can you add something to it, why do you suggest it? Is their description of Polylogarithms interesting? $\endgroup$
    – nicoguaro ♦
    Commented Sep 2, 2016 at 21:19
  • $\begingroup$ Would you mind telling where exactly it is to be found? I have checked both the 2nd and 3rd edition, and there are no polylogarithms there. $\endgroup$
    – TomR
    Commented Jul 24, 2020 at 11:14
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A great algorithm for this, including the analytic continuation, is provided here. It is rare that I recommend to write these things yourself, but in this case it is very straightforward.

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