Ramanujan tau theta function: Series representations (formula 10.12.06.0030)

RamanujanTauTheta

$Mathematica Notation$

Zeta Functions and Polylogarithms

RamanujanTauTheta[z]

Series representations

Generalized power series

Expansions at z==-6i-i n

http://functions.wolfram.com/10.12.06.0030.01

Input Form

RamanujanTauTheta[z] \[Proportional] (-(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] - (1/2) I Log[n! (n + 11)!] + (1/2) (-2 Log[2 Pi] + PolyGamma[1 + n] + PolyGamma[12 + n]) (z + I (6 + n)) - (I/4) (Pi^2/3 - PolyGamma[1, 1 + n] - PolyGamma[1, 12 + n]) (z + I (6 + n))^2 + O[(z + I (6 + n))^3] /; 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