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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/10.03.21.0004.01









  


  










Input Form





Integrate[z^n RiemannSiegelTheta[a + b z], z] == (-(1/2)) z^(1 + n) (a/(1 + n) + (b z)/(2 + n)) Log[Pi] - ((n! z^n)/b) Sum[((1/(n - k)!) ((-1)^k PolyGamma[-2 - k, 1/4 + (I a)/2 + ((I b)/2) z] + PolyGamma[-2 - k, 1/4 - (I a)/2 - ((I b)/2) z]))/ ((I b z)/2)^k, {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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