Zeta Functions & Polylogarithms - Wolfram Mathematica 8 Documentation

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.

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

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Analytic Number Theory

Number Theoretic Functions

Special Functions

Prime Numbers