Lerch transcendent: Specific values (formula 10.06.03.0061)

LerchPhi

$Mathematica Notation$

Zeta Functions and Polylogarithms

http://functions.wolfram.com/10.06.03.0061.01

Input Form

LerchPhi[z, 3, a] == (1/a^3) (HypergeometricPFQ[{1, a, a, a}, {1 + a, 1 + a, 1 + a}, z] (1 - 2 UnitStep[-Re[a]])) + (2 ((z HypergeometricPFQ[{1, 1 + a - Ceiling[Re[a]], 1 + a - Ceiling[Re[a]], 1 + a - Ceiling[Re[a]]}, {2 + a - Ceiling[Re[a]], 2 + a - Ceiling[Re[a]], 2 + a - Ceiling[Re[a]]}, z])/(1 + a - Ceiling[Re[a]])^3 + ((1 - Ceiling[Re[a]] + Floor[Re[a]]) UnitStep[Im[a]])/ ((a - Ceiling[Re[a]])^2)^(3/2)) UnitStep[-Re[a]])/z^Ceiling[Re[a]]

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