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RiemannSiegelTheta






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/10.03.06.0017.01









  


  










Input Form





RiemannSiegelTheta[z] \[Proportional] -((Pi Sqrt[z^2])/(8 z)) - (z/2) (1 + Log[Pi]) + (z/4) Log[z^2/4] + Sum[((-1)^k ((4 k + 3)/(16 (k + 1) (2 k + 1)) - 2 Sum[(2^(4 j) (2 k)! BernoulliB[2 + 2 j])/((2 j + 2)! (2 k - 2 j)!), {j, 0, k - 1}]) z^(-2 k - 1))/2^(2 k), {k, 0, Infinity}] /; Abs[Arg[z^2]] < Pi && (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)





2001-10-29





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