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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/06.01.06.0011.01









  


  










Input Form





(n + a)!/(n + b)! \[Proportional] n^(a - b) Sum[((-1)^k Pochhammer[b - a, k] B[k, a - b + 1, a + 1])/ (n^k k!), {k, 0, Infinity}] /; Abs[Arg[n + a + 1]] < Pi && (Abs[n] -> Infinity) && B[n, \[Alpha], z] == n! SeriesTerm[(t^\[Alpha] E^(t z))/(E^t - 1)^\[Alpha], {t, 0, n}]










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





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