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RiemannSiegelTheta






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/10.03.21.0003.01









  


  










Input Form





Integrate[z^n RiemannSiegelTheta[z], z] == -((z^(2 + n) Log[Pi])/(2 (2 + n))) - z^n n! Sum[(2^k/((I z)^k (n - k)!)) (PolyGamma[-2 - k, 1/4 - (I z)/2] + (-1)^k PolyGamma[-2 - k, 1/4 + (I z)/2]), {k, 0, n}] /; Element[n, Integers] && n >= 0










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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