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RiemannSiegelTheta




Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > RiemannSiegelTheta[z] > Series representations > Generalized power series > Expansions at z==-i/2





http://functions.wolfram.com/10.03.06.0007.01









  


  








Input Form





RiemannSiegelTheta[z] == (-(I/2)) Log[(-(I/2)) (z + I/2)] - ((EulerGamma + Log[2 Pi])/2) (z + I/2) - (I/8) Sum[(Zeta[2 + j]/(2 + j)) ((I/2)^j + (-(I/2))^j - 4 (-I)^j) (z + I/2)^(2 + j), {j, 0, Infinity}] /; Abs[z + I/2] < 2








Standard Form





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MathML Form







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</mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[EulerGamma]] </annotation> </semantics> </mrow> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mfrac> <mi> &#8520; </mi> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mi> &#8520; </mi> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> &#8734; </mi> </munderover> <mrow> <mfrac> <mrow> <mtext> </mtext> <semantics> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> j </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Zeta]&quot;, &quot;(&quot;, TagBox[RowBox[List[&quot;j&quot;, &quot;+&quot;, &quot;2&quot;]], Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[$CellContext`e, Zeta[$CellContext`e]]]] </annotation> </semantics> </mrow> <mrow> <mi> j </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </mfrac> <mo> &#8290; 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Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-10-29