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RamanujanTauTheta






Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > RamanujanTauTheta[z] > Series representations > Asymptotic series expansions





http://functions.wolfram.com/10.12.06.0033.01









  


  










Input Form





RamanujanTauTheta[z] \[Proportional] z Log[z] + (-1 - Log[2 Pi] + Pi I Floor[(Pi - 2 Arg[z])/(4 Pi)] + Pi I Floor[3/4 - Arg[z]/(2 Pi)]) z + (11 Pi)/4 + ((11 Pi)/2) Floor[(Pi - 2 Arg[z])/(4 Pi)] - ((11 Pi)/2) Floor[3/4 - Arg[z]/(2 Pi)] - (1/z) Sum[((-1)^k 6^(2 k) (33/(2 k + 1) - 18/(k + 1) + Sum[((2 k)! BernoulliB[1 + 2 j])/(6^(2 j) (2 (1 + j) (2 j + 1)! (2 k - 2 j)!)), {j, 0, k}]))/z^(2 k), {k, 0, Infinity}] /; (Abs[z] -> Infinity)










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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