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InverseJacobiND






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.44.20.0010.01









  


  










Input Form





D[InverseJacobiND[z, m], {m, \[Alpha]}] == I Sum[(1/(k! Gamma[k - \[Alpha] + 1])) Pochhammer[1/2, k]^2 (PolyGamma[k + 1] - PolyGamma[1/2 + k]) m^k, {k, 0, Infinity}] - (I/(m^\[Alpha] 2)) Sum[(Pochhammer[1/2, k]^2 FDLogConstant[m, k, \[Alpha]] m^k)/k!^2, {k, 0, Infinity}] - ((I z Sqrt[Pi])/(m^\[Alpha] (2 Sqrt[1 - z^2]))) HypergeometricPFQRegularized[{{1/2}, {1/2}, {1/2, 1}}, {{3/2}, {}, {1 - \[Alpha]}}, z^2/(z^2 - 1), (m z^2)/(z^2 - 1)] /; -1 < z < 1 && -1 < m < 1










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