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JacobiCS




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.27.20.0006.01









  


  








Input Form





D[JacobiCS[z, m], {z, \[Alpha]}] == FDPowerConstant[z, -1, \[Alpha]] z^(-\[Alpha] - 1) + (1/2) Sum[((-1)^k Pi^(2 k) BernoulliB[2 k] z^(2 k - \[Alpha] - 1))/ (EllipticK[m]^(2 k) (k Gamma[2 k - \[Alpha]])), {k, 1, Infinity}] - ((2^\[Alpha] Pi^(5/2) z^(1 - \[Alpha]))/EllipticK[m]^2) Sum[((k EllipticNomeQ[m]^(2 k))/(EllipticNomeQ[m]^(2 k) + 1)) HypergeometricPFQRegularized[{1}, {1 - \[Alpha]/2, (3 - \[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