Zeta Functions & Polylogarithms

The Wolfram Language supports zeta and polylogarithm functions of a complex variable in full generality, performing efficient arbitrary-precision evaluation and implementing extensive symbolic transformations.

Zeta Riemann and generalized Riemann zeta function

RiemannSiegelZ  ▪  RiemannSiegelTheta  ▪  StieltjesGamma  ▪  RiemannXi

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

DirichletBeta  ▪  DirichletEta  ▪  DirichletLambda

PrimeZetaP prime zeta function

FunctionExpand expand out symbolic forms of functions