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MATHEMATICA GUIDE
Zeta Functions & Polylogarithms
Mathematica supports zeta and polylogarithm functions of a complex variable in full generality, performing efficient arbitrary-precision evaluation and implementing extensive symbolic transformations.
Reference
Zeta — Riemann and generalized Riemann zeta function
RiemannSiegelZ ▪ RiemannSiegelTheta ▪ StieltjesGamma
ZetaZero — zeros of the zeta function on the critical line
PolyLog — ordinary and Nielsen generalized polylogarithm function
LerchPhi — Lerch 
function
HurwitzZeta, HurwitzLerchPhi — functions with original Hurwitz analytic structure
PrimeZetaP — prime zeta function
FunctionExpand — expand out symbolic forms of functions
