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Subfactorial






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Subfactorial[n] > Differentiation > Symbolic differentiation





http://functions.wolfram.com/06.42.20.0007.01









  


  










Input Form





D[Subfactorial[z], {z, n}] == (1/E) (Derivative[n][Gamma][z + 1] + (-1)^z Sum[(-1)^(n - j) Binomial[n, j] (n - j)! Gamma[z + 1]^(n - j + 1) (Pi I)^j HypergeometricPFQRegularized[{Subscript[a, 1], Subscript[a, 2], \[Ellipsis], Subscript[a, n - j + 1]}, {1 + Subscript[a, 1], 1 + Subscript[a, 2], \[Ellipsis], 1 + Subscript[a, n - j + 1]}, 1], {j, 0, n}]) /; Subscript[a, 1] == Subscript[a, 2] == \[Ellipsis] == Subscript[a, n + 1] == z + 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)





2007-05-02





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