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Subfactorial






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Subfactorial[n] > Series representations > Asymptotic series expansions





http://functions.wolfram.com/06.42.06.0007.01









  


  










Input Form





Subfactorial[z] \[Proportional] (1/E) ((z (Csc[z Pi]/2)^Floor[(Pi + Arg[z])/(2 Pi)] Sqrt[2 Pi] (Exp[Pi I Floor[(Pi + Arg[z])/(2 Pi)]] z)^(z - 1/2) Exp[Sum[BernoulliB[2 + 2 k]/(2 (1 + k) (2 k + 1) z^(2 k + 1)), {k, 0, Infinity}]])/E^z - (1 - E) (-1)^z - (-1)^z Sum[(-j)^k/j!/z^k, {k, 0, Infinity}, {j, 1, Infinity}]) /; !(Element[z, Integers] && z < 1) && (Abs[z] -> Infinity)










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