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RiemannSiegelTheta






Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > RiemannSiegelTheta[z] > Specific values > Specialized values





http://functions.wolfram.com/10.03.03.0018.01









  


  










Input Form





RiemannSiegelTheta[(I (4 p - q))/(2 q) - 2 I n] == (I/(2 q)) (q Log[2] + n q ((-I) Pi + Log[2] + 2 Log[Pi q]) - 2 p Log[2 Pi] + q Log[Cos[(p Pi)/q] Gamma[(2 p)/q]] - q Sum[Log[2 q k - q - 2 p], {k, 1, n}] - q Sum[Log[q k - p], {k, 1, n}]) /; Element[n, Integers] && n >= 0 && Element[p, Integers] && p > 0 && Element[q, Integers] && q > 0 && p < q










Standard Form





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MathML Form







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</mo> <mi> p </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> <mo> &#8290; </mo> <mi> q </mi> </mrow> <mo> - </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> n </mi> <mo> &#8712; </mo> <semantics> <mi> &#8469; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalN]&quot;, Function[Integers]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mi> p </mi> <mo> &#8712; </mo> <semantics> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> <annotation encoding='Mathematica'> TagBox[SuperscriptBox[&quot;\[DoubleStruckCapitalN]&quot;, &quot;+&quot;], Function[Integers]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mi> q </mi> <mo> &#8712; </mo> <semantics> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> <annotation encoding='Mathematica'> TagBox[SuperscriptBox[&quot;\[DoubleStruckCapitalN]&quot;, &quot;+&quot;], Function[Integers]] </annotation> </semantics> </mrow> <mo> &#8743; 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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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