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variants of this functions
EllipticPi




Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticPi[n,z,m] > Differentiation > Symbolic differentiation > With respect to n





http://functions.wolfram.com/08.06.20.0013.01









  


  








Input Form





D[EllipticPi[n, z, m], {n, p}] == ((Sin[z]^(2 p + 1) p!)/(2 p + 1)) Sum[((Pochhammer[1/2 + p, Subscript[k, 1] + Subscript[k, 2] + Subscript[k, 3]] Pochhammer[p + 1, Subscript[k, 1]])/ (Pochhammer[3/2 + p, Subscript[k, 1] + Subscript[k, 2] + Subscript[k, 3]] Subscript[k, 1]! Subscript[k, 2]! Subscript[k, 3]!)) Pochhammer[1/2, Subscript[k, 2]] Pochhammer[1/2, Subscript[k, 3]] n^Subscript[k, 1] Sin[z]^(2 (Subscript[k, 1] + Subscript[k, 2] + Subscript[k, 3])) m^Subscript[k, 3], {Subscript[k, 1], p, Infinity}, {Subscript[k, 2], 0, Infinity}, {Subscript[k, 3], 0, Infinity}] /; Element[p, Integers] && p >= 0








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)





2007-05-02