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Binomial






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Binomial[n,k] > Series representations > Asymptotic series expansions > Expansions at n==infinity





http://functions.wolfram.com/06.03.06.0002.01









  


  










Input Form





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










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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