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JacobiDN




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.29.20.0007.01









  


  








Input Form





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