The Hurwitz zeta function ζ(s, a) is a generalization of the Riemann zeta function ζ(s) that is also known as the generalized zeta function. It is classically defined by the formula ζ(s, a) congruent sum_(k = 0)^∞ 1/(k + a)^s for ℜ[s]>1 and by analytic continuation to other s!=1, where any term with k + a = 0 is excluded. It is implemented in this form in the Wolfram Language as HurwitzZeta[s, a].
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