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Multinomial






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Multinomial[n1,n2,...,nm] > Series representations > Asymptotic series expansions





http://functions.wolfram.com/06.04.06.0001.01









  


  










Input Form





Multinomial[Subscript[n, 1], Subscript[n, 2], \[Ellipsis], Subscript[n, m]] \[Proportional] (Subscript[n, 1]^(a - 1)/Product[Gamma[Subscript[n, k] + 1], {k, 2, m}]) Sum[((((-1)^k Pochhammer[1 - a, k])/k!) B[k, a, a])/Subscript[n, 1]^k, {k, 0, Infinity}] /; (Abs[Subscript[n, 1]] -> Infinity) && a == 1 + Sum[Subscript[n, k], {k, 2, m}] && B[n, \[Alpha], z] == n! SeriesTerm[(t^\[Alpha] E^(t z))/(E^t - 1)^\[Alpha], {t, 0, n}] && Abs[Arg[Subscript[n, 1] + a]] < 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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