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JacobiDC




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.28.20.0006.01









  


  








Input Form





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