Lerch transcendent: Integral representations (formula 10.06.07.0005)

LerchPhi

$Mathematica Notation$

Zeta Functions and Polylogarithms

LerchPhi[z,s,a]

Integral representations

Contour integral representations

For Phi^{^}(z,s,a)

http://functions.wolfram.com/10.06.07.0005.01

Input Form

LerchPhiClassical[z, s, a - n] == (z^n/(2 I)) Integrate[Csc[Pi t]/((a - t)^s (-z)^t), {t, \[Gamma] - I Infinity, \[Gamma] + I Infinity}] /; Element[n, Integers] && n < \[Gamma] < n + 1 && Re[a] > \[Gamma] && z != 0 && (Arg[-z] < Pi || Re[s] > 1)

Standard Form

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MathML Form

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Rule Form

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Contributed by

Allan Cortzen

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

2002-12-18