Ramanujan tau theta function: Series representations (formula 10.12.06.0031)

RamanujanTauTheta

$Mathematica Notation$

Zeta Functions and Polylogarithms

RamanujanTauTheta[z]

Series representations

Generalized power series

Expansions at z==-6i-i n

http://functions.wolfram.com/10.12.06.0031.01

Input Form

RamanujanTauTheta[z] == (-(I/2)) Log[(-I) (z + I (6 + n))] + (n Pi)/2 + n Pi Floor[Arg[(-I) (z + I (6 + n))]/(2 Pi)] + I (6 + n) Log[2 Pi] + (I/2) Sum[((-I)^k/k!) ((1 + (-1)^k) PolyGamma[-1 + k, 1] - (-1)^k (PolyGamma[-1 + k, 1 + n] + PolyGamma[-1 + k, 12 + n]) - 2 KroneckerDelta[k - 1] Log[2 Pi]) (z + I (6 + n))^k, {k, 0, Infinity}] /; Abs[z + I (6 + n)] < 1 && Element[n, Integers] && n >= 0

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