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RamanujanTauTheta






Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > RamanujanTauTheta[z] > Integral representations > On the real axis > Of the direct function





http://functions.wolfram.com/10.12.07.0005.01









  


  










Input Form





RamanujanTauTheta[z] == -z - z Log[2 Pi] + ((11 I + 2 z) Log[6 - I z] - 11 I Log[6 + I z])/4 + (z/2) Log[6 + I z] - I Integrate[(ArcTan[t/(6 + I z)] - I ArcTanh[t/(6 I + z)])/ (-1 + E^(2 Pi t)), {t, 0, Infinity}] /; Abs[Im[z]] < 6










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





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