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
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++.