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JacobiNS




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.33.20.0006.01









  


  








Input Form





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