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JacobiZeta




Mathematica Notation

Traditional Notation









Elliptic Integrals > JacobiZeta[z,m] > Differentiation > Fractional integro-differentiation > With respect to z





http://functions.wolfram.com/08.07.20.0007.01









  


  








Input Form





D[JacobiZeta[z, m], {z, \[Alpha]}] == z^(1 - \[Alpha]) Sqrt[Pi] 2^\[Alpha] Sum[((-1)^k/k!) (Pochhammer[-(1/2), k] Hypergeometric2F1[k - 1/2, k + 1/2, 2 k + 1, m] - (EllipticE[m]/EllipticK[m]) Pochhammer[1/2, k] Hypergeometric2F1[k + 1/2, k + 1/2, 2 k + 1, m]) HypergeometricPFQRegularized[{1}, {1 - \[Alpha]/2, (3 - \[Alpha])/2}, (-k^2) z^2] (m/4)^k, {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