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Multinomial




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Multinomial[n1,n2,...,nm] > Differentiation > Symbolic differentiation





http://functions.wolfram.com/06.04.20.0003.02









  


  








Input Form





D[Multinomial[Subscript[n, 1], Subscript[n, 2], \[Ellipsis], Subscript[n, m]], {Subscript[n, m], u}] == (((-1)^u u! Gamma[s + 1]^(u + 1))/Product[Gamma[Subscript[n, k] + 1] Gamma[Subscript[n, m] - s], {k, 1, m - 1}]) HypergeometricPFQRegularized[{Subscript[a, 1], Subscript[a, 2], \[Ellipsis], Subscript[a, u + 1], s - Subscript[n, m] + 1}, {1 + Subscript[a, 1], 1 + Subscript[a, 2], \[Ellipsis], 1 + Subscript[a, u + 1]}, 1] /; Subscript[a, 1] == Subscript[a, 2] == \[Ellipsis] == Subscript[a, u + 1] == s + 1 && s == Sum[Subscript[n, k], {k, 1, m}] && Element[u, Integers] && u >= 0 && !(Element[s - Subscript[n, m], Integers] && s - Subscript[n, m] >= 0)








Standard Form





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MathML Form







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</ci> <apply> <ci> Subscript </ci> <ci> a </ci> <apply> <plus /> <ci> u </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <plus /> <ci> s </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> n </ci> <ci> m </ci> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </list> <list> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <ci> &#8230; </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <apply> <plus /> <ci> u </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </list> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <and /> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <ci> &#8230; 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Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-10-29