search

MartinMikkelsen / FewSpecialFunctions.jl

Few special functions in Julia. Includes Clausen function, Coulomb wave functions, Debye function, Fresnel functions, Struve function, Hypergeometric functions, Confluent hypergeometric functions, Fermi-Dirac
https://martinmikkelsen.github.io/FewSpecialFunctions.jl/dev
MIT License
13 stars 2 forks source link

Polylogarithm #6

Open MartinMikkelsen opened 1 year ago

MartinMikkelsen commented 1 year ago

Implement the polylogarithm (maybe just the dilogarithm at first). Perhaps using the following integral representation

\text{Li}_s(z)= \frac{z}{\Gamma(s)} \int_0^1 \frac{|\log(y)^{s-1}|}{1-yz} \, \text{d}y

Consider branch at $z=1$.

Numerical implementation Polylogarithm