zeta — Math

The Riemann zeta function of z in Math, is special function. Defined by

$\zeta(z) = \sum_{k=1}^\infty \frac{ 1 }{ k^z }$

$\zeta(z,n) = \sum_{k=0}^\infty \frac{ 1 }{ (k+n)^z }$

hurwitzZeta( x, a ) = zeta(x,a) — Hurwitz zeta function of a real or complex number with real or complex parameter a.
zeta(z,1) = zeta(z)
zeta(n,x) = polygamma(n-1,x) when n>1 and x>0.

Real part on the real axis:

Imaginary part on the real axis is zero.

Real part on the imaginary axis:

Imaginary part on the imaginary axis:

Real part on the complex plane:

Imaginary part on the complex plane:

Absolute value on the complex plane:

Reference

Related functions: dirichletEta logGamma

Function category: zeta functions