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variants of this functions
EllipticE






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/08.04.20.0009.01









  


  










Input Form





D[EllipticE[z, m], {z, \[Alpha]}] == EllipticE[m]/(z^\[Alpha] Gamma[1 - \[Alpha]]) - (2^\[Alpha] Sqrt[Pi] (Sum[(((-m)^j 2^(-2 j - 2 n))/((n + j)! j! (2 j + 2 n + 1))) Pochhammer[-(1/2), j] Pochhammer[1/2, j] Pochhammer[1/2, n] Sum[Binomial[2 j + 2 n + 1, k] HypergeometricPFQRegularized[{1}, {(1 - \[Alpha])/2, 1 - \[Alpha]/2}, -(((1 + 2 j + 2 n - 2 k)^2 z^2)/ 4)], {k, 0, j + n}], {n, 0, Infinity}, {j, 0, Infinity}] - (m/2) Sum[(((-1)^j m^(j + n))/(2^(2 j) ((2 j + 1) j! Pochhammer[2, n + j] Pochhammer[3/2, n]))) Pochhammer[1/2, n + j] Pochhammer[3/2, n + j] Sum[Binomial[2 j + 1, k] HypergeometricPFQRegularized[{1}, {(1 - \[Alpha])/2, 1 - \[Alpha]/2}, -(((1 + 2 j - 2 k)^2 z^2)/4)], {k, 0, j}], {n, 0, Infinity}, {j, 0, Infinity}]))/z^\[Alpha]










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





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