Hurwitz zeta function: Representations through equivalent functions (formula 10.02.27.0008)

Zeta

$Mathematica Notation$

Zeta Functions and Polylogarithms

Zeta[s,a]

Representations through equivalent functions

Interrelations

http://functions.wolfram.com/10.02.27.0008.01

Input Form

ZetaClassical[s, a] == Zeta[s, a]/E^(UnitStep[Floor[-Re[a]]] (2 UnitStep[Im[a]] - 1) Pi I s) + UnitStep[Floor[-Re[a]]] (1 - E^((-(2 UnitStep[Im[a]] - 1)) Pi I s)) ((UnitStep[Im[a]] (1 + Floor[-Re[a]] + Floor[Re[a]]))/ ((Floor[-Re[a]] + a)^2)^(s/2) + Zeta[s, a + Floor[-Re[a]] + 1])

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

Zeta[s]