`hurwitzZeta`

Hurwitz zeta function.

Category: Mathematics > Mathematical Functions

Syntax

Z = hurwitzZeta(s, a)

Evaluates the sum of 1/(k + a)^s for k = 0, 1, 2, ...

Description

For a = 1 the Hurwitz zeta function is the Riemann zeta function, so hurwitzZeta(2, 1) is pi^2/6. For other offsets the terms are shifted along the number line: hurwitzZeta(s, 0.5) equals (2^s - 1)*zeta(s). It generalizes zeta and is related to the polygamma functions.

Input arguments

s: Exponent, with s > 1 for convergence of the sum.
a: Offset, a > 0.

Output arguments

Z: Array formed by broadcasting s and a.

Example

Zeta as a special case

hurwitzZeta(2, 1)
pi^2/6
hurwitzZeta(3, 0.5)
(2^3 - 1)*zeta(3)

Output

ans = 1.6449
ans = 1.6449
ans = 8.4144
ans = 8.4144

See also

zeta psi gamma dilog