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Subfactorial




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Subfactorial[n] > Series representations > Generalized power series > Expansions at generic point z==z0





http://functions.wolfram.com/06.42.06.0003.01









  


  








Input Form





Subfactorial[z] == (1/E) Sum[(1/k!) (Derivative[k][Gamma][Subscript[z, 0] + 1] + (-1)^Subscript[z, 0] Sum[(-1)^(k - j) Binomial[k, j] (k - j)! Gamma[Subscript[z, 0] + 1]^(k - 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, k}]) (z - Subscript[z, 0])^k, {k, 0, Infinity}] /; Subscript[a, 1] == Subscript[a, 2] == \[Ellipsis] == Subscript[a, k + 1] == Subscript[z, 0] + 1 && Element[k, Integers] && k >= 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