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Subfactorial




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Subfactorial[n] > Differentiation > Low-order differentiation





http://functions.wolfram.com/06.42.20.0004.01









  


  








Input Form





D[Subfactorial[z], {z, 2}] == (1/E) ((-Pi^2) Gamma[1 + z, -1] + ((2 (-1)^z)/(1 + z)^3) ((-I) Pi (1 + z) HypergeometricPFQ[{1 + z, 1 + z}, {2 + z, 2 + z}, 1] + HypergeometricPFQ[{1 + z, 1 + z, 1 + z}, {2 + z, 2 + z, 2 + z}, 1]) + Gamma[1 + z] (Pi^2 + PolyGamma[1 + z]^2 + PolyGamma[1, 1 + z]))








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