Ramanujan tau theta function: Integration (formula 10.12.21.0005)

RamanujanTauTheta

$Mathematica Notation$

Zeta Functions and Polylogarithms

RamanujanTauTheta[z]

Integration

Definite integration

For the direct function itself

http://functions.wolfram.com/10.12.21.0005.01

Input Form

Integrate[RamanujanTauTheta[t], {t, z, z + 1}] == (1/2) (-Log[2 Pi] - 2 z Log[2 Pi] + PolyGamma[-2, 6 - I z] + PolyGamma[-2, 6 + I z] - PolyGamma[-2, (6 + I) + I z] - PolyGamma[-2, (-I) ((1 + 6 I) + z)]) /; !IntervalMemberQ[Interval[{-Infinity, -6}], I z] && !IntervalMemberQ[Interval[{6, Infinity}], I z]

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