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variants of this functions
Factorial






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/06.01.06.0008.01









  


  










Input Form





n! \[Proportional] (Sqrt[2 Pi] n^(n + 1/2) (1 + 1/(12 n) + 1/(288 n^2) - 139/(51840 n^3) - 571/(2488320 n^4) + 163879/(209018880 n^5) + 5246819/(75246796800 n^6) - 534703531/(902961561600 n^7) - 4483131259/(86684309913600 n^8) + 432261921612371/ (514904800886784000 n^9) + O[1/n^10]))/E^n /; Abs[Arg[n]] < Pi && (Abs[n] -> 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)





2001-10-29