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RiemannSiegelTheta






Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > RiemannSiegelTheta[z] > Integration > Indefinite integration > Involving only one direct function





http://functions.wolfram.com/10.03.21.0001.01









  


  










Input Form





Integrate[RiemannSiegelTheta[z], z] == Sum[z^2/(4 k) + (1/4) ((1 + 4 k - 2 I z) Log[1 - (2 I z)/(1 + 4 k)] + (1 + 4 k + 2 I z) Log[1 + (2 I z)/(1 + 4 k)]), {k, 1, Infinity}] - ((Log[Pi] + EulerGamma) z^2)/4 + ((1 - 2 I z) Log[1 - 2 I z] + (1 + 2 I z) Log[1 + 2 I z])/4










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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