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JacobiZeta






Mathematica Notation

Traditional Notation









Elliptic Integrals > JacobiZeta[z,m] > Differentiation > Symbolic differentiation > With respect to z





http://functions.wolfram.com/08.07.20.0005.01









  


  










Input Form





D[JacobiZeta[z, m], {z, n}] == ((-(((2 I)^(n - 1) Sqrt[Pi])/Sqrt[1 - m Sin[z]^2])) Sum[(((E^(2 I k z) StirlingS2[n - 1, k])/Gamma[3/2 - k]) ((EllipticE[m]/EllipticK[m]) (2 k - 1) m (2 - 2 Sqrt[1 - m] + (E^(2 I z) - 1) m) AppellF1[1/2, -(1/2), 1/2, 1/2 - k, (2 + 2 Sqrt[1 - m] + (E^(2 I z) - 1) m)/(2 + 2 Sqrt[1 - m] - m), (2 + 2 Sqrt[1 - m] + (E^(2 I z) - 1) m)/(4 Sqrt[1 - m])] - (m - 2 E^(2 I z) (m - 2) + E^(4 I z) m) (2 - 2 Sqrt[1 - m] + (Sqrt[1 - m] - 2) m) AppellF1[3/2, 1/2, -(1/2), 3/2 - k, (2 + 2 Sqrt[1 - m] + (E^(2 I z) - 1) m)/(2 + 2 Sqrt[1 - m] - m), (2 + 2 Sqrt[1 - m] + (E^(2 I z) - 1) m)/(4 Sqrt[1 - m])]))/ (((E^(2 I z) - 1) m + 2 Sqrt[1 - m] + 2)/m)^k, {k, 0, n - 1}])/ (((E^(2 I z) (m + 2 Sqrt[1 - m] - 2))/m)^2^(-1) ((m[1 - E^(2 I z)] + 2 Sqrt[1 - m] - 2)/Sqrt[1 - m])^2^(-1)) /; Element[n, Integers] && n > 0










Standard Form





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MathML Form







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&#8290; </mo> <mi> z </mi> </mrow> </msup> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> m </mi> </mrow> </msqrt> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> m </mi> </mrow> </msqrt> </mrow> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <semantics> <msub> <mi> F </mi> <mn> 1 </mn> </msub> <annotation-xml encoding='MathML-Content'> <ci> AppellF1 </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> <mo> ; </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 3 </mn> <mn> 2 </mn> 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Rule Form





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





2001-10-29





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