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variants of this functions
Gamma




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/06.05.06.0012.01









  


  








Input Form





Gamma[z] \[Proportional] (Sqrt[2 Pi] z^(z - 1/2) (1 + Sum[((-1)^j PermutationCyclesD[2 (k + j), j])/(2^(k + j) (k + j)!)/ z^k, {k, 1, Infinity}, {j, 1, 2 k}]))/E^z /; (Abs[Arg[z]] < Pi && (Abs[z] -> Infinity) && PermutationCyclesD[n, j] == (n - 1) (PermutationCyclesD[n - 1, j] + (n - 2) PermutationCyclesD[n - 3, j - 1]) && PermutationCyclesD[0, 0] == 1 && PermutationCyclesD[n, 1] == (n - 1)! && PermutationCyclesD[n, j] == 0 /; n <= 3 j - 1)








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)





2001-10-29