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JacobiCD




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.25.20.0006.01









  


  








Input Form





D[JacobiCD[z, m], {z, \[Alpha]}] == ((2^(\[Alpha] + 1) Pi^(3/2))/(z^\[Alpha] (Sqrt[m] EllipticK[m]))) Sum[(((-1)^k EllipticNomeQ[m]^(k + 1/2))/(1 - EllipticNomeQ[m]^(2 k + 1))) HypergeometricPFQRegularized[{1}, {(1 - \[Alpha])/2, 1 - \[Alpha]/2}, -(((1 + 2 k)^2 Pi^2 z^2)/(16 EllipticK[m]^2))], {k, 0, Infinity}]








Standard Form





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MathML Form







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</mi> </munderover> <mrow> <mfrac> <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> <mrow> <mi> k </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </msup> </mrow> <mrow> <mn> 1 </mn> <mo> - </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> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> </mrow> </mfrac> <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> ; 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Rule Form





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





2001-10-29