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JacobiND






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.32.20.0006.01









  


  










Input Form





D[JacobiND[z, m], {z, \[Alpha]}] == Pi/(z^\[Alpha] (2 Sqrt[1 - m] EllipticK[m] Gamma[1 - \[Alpha]])) + ((2^(\[Alpha] + 1) Pi^(3/2))/(z^\[Alpha] (Sqrt[1 - m] EllipticK[m]))) Sum[(((-1)^k EllipticNomeQ[m]^k)/(EllipticNomeQ[m]^(2 k) + 1)) HypergeometricPFQRegularized[{1}, {(1 - \[Alpha])/2, 1 - \[Alpha]/2}, -((k^2 Pi^2 z^2)/(4 EllipticK[m]^2))], {k, 1, Infinity}]










Standard Form





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MathML Form







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Rule Form





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





2001-10-29