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NevilleThetaN






Mathematica Notation

Traditional Notation









Elliptic Functions > NevilleThetaN[z,m] > Differentiation > Fractional integro-differentiation > With respect to z





http://functions.wolfram.com/09.11.20.0004.01









  


  










Input Form





D[NevilleThetaN[z, m], {z, \[Alpha]}] == ((Sqrt[Pi]/(Sqrt[2] (1 - m)^(1/4) Sqrt[EllipticK[m]])) (1/Gamma[1 - \[Alpha]] + 2^(\[Alpha] + 1) Sqrt[Pi] Sum[(-1)^k EllipticNomeQ[m]^k^2 HypergeometricPFQRegularized[{1}, {(1 - \[Alpha])/2, 1 - \[Alpha]/2}, -((k^2 Pi^2 z^2)/(4 EllipticK[m]^2))], {k, 1, Infinity}]))/z^\[Alpha]










Standard Form





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MathML Form







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</mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> &#8734; </mi> </munderover> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> <mo> &#8290; </mo> <msup> <mrow> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <msup> <mi> k </mi> <mn> 2 </mn> </msup> </msup> <mo> &#8290; </mo> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mn> 1 </mn> </msub> <msub> <mover> <mi> F </mi> <mo> ~ </mo> </mover> <mn> 2 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> ; </mo> <mrow> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#945; </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mi> &#945; 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</ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29