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RiemannSiegelTheta






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/10.03.06.0019.01









  


  










Input Form





RiemannSiegelTheta[z] == (-(Log[Pi]/2)) z - (1/2) EulerGamma z - (I/2) Log[1 - 2 I z] + (I/2) Log[1 + 2 I z] - (I/4) Log[(Pi (1/4 + (I z)/2))/Sin[Pi (1/4 + (I z)/2)]] + (I/4) Log[(Pi (1/4 - (I z)/2))/Sin[Pi (1/4 - (I z)/2)]] - (1/2) Sum[((-1)^(j + k) 2^(-2 j - 2 k) z^(1 - 2 j + 2 k) (2 k)! Zeta[1 + 2 k])/((2 j)! (2 k - 2 j + 1)!), {k, 1, Infinity}, {j, 0, k}] /; Abs[z] < 2










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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