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.

(RefLink[Zeta, paclet:ref/Zeta]) — Riemann and generalized Riemann zeta function

(RefLink[ZetaZero, paclet:ref/ZetaZero]) — zeros of the zeta function on the critical line

(RefLink[PolyLog, paclet:ref/PolyLog]) — ordinary and Nielsen generalized polylogarithm function

(RefLink[LerchPhi, paclet:ref/LerchPhi]) — Lerch Φ function

(RefLink[HurwitzZeta, paclet:ref/HurwitzZeta]), (RefLink[HurwitzLerchPhi, paclet:ref/HurwitzLerchPhi]) — functions with original Hurwitz analytic structure

(RefLink[PrimeZetaP, paclet:ref/PrimeZetaP]) — prime zeta function

(RefLink[FunctionExpand, paclet:ref/FunctionExpand]) — expand out symbolic forms of functions