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variants of this functions
Hypergeometric2F1Regularized




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1Regularized[a,b,c,z] > Differentiation > Symbolic differentiation > With respect to element of parameters ||| With respect to element of parameters





http://functions.wolfram.com/07.24.20.0048.02









  


  








Input Form





D[Hypergeometric2F1Regularized[a, b, a + 1, z], {a, n}] == D[1/Gamma[a + 1], {a, n}]/(1 - z)^b - n! z b Sum[(((-1)^k Gamma[a + 1]^(k + 1))/(n - k)!) D[1/Gamma[a + 1], {a, n - k}] HypergeometricPFQRegularized[ {Subscript[c, 1], \[Ellipsis], Subscript[c, k + 1], b + 1}, {Subscript[c, 1] + 1, \[Ellipsis], Subscript[c, k + 1] + 1}, z], {k, 0, n}] /; Subscript[c, 1] == Subscript[c, 2] == \[Ellipsis] == Subscript[c, k + 1] == a + 1 && Element[n, Integers] && n >= 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)





2003-08-21