A repository for the implementation of the Hurwitz Zeta, PolyLog and related functions. In the hope that it will make its way into gcc.
The series expansions in this code are based on the excellent paper by David C. Wood, The computation of Polylogarithms
Other sources are the wikipedia.
ideas:
- Use Kahan summation for improved stability. The runtime will likely be dominated by function evluations.
- Generally a function for zeta at the integers.
- We're evaluating the Zeta function on positive integers. Try to use an efficient series for the Bernoulli Numbers for that.
- norm(z) vs. abs(z) abs on complex numbers involves a sqrt. whereas abs on reals is just an if(). On the other hand the magnitude of the numbers returned by the norm is quadratically bigger. Therefore the resulting comparison is less precise.
- Better stability for large index s