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Binomial




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Binomial[n,k] > Series representations > Generalized power series > Expansions at generic point k==k0 > For the function itself





http://functions.wolfram.com/06.03.06.0017.01









  


  








Input Form





Binomial[n, k] == Gamma[Subscript[k, 0] - n] Sum[(Pi^(m - 1)/m!) Sum[Binomial[m, j] Sin[Pi (Subscript[k, 0] - n + (m - j)/2)] j! HypergeometricPFQRegularized[{Subscript[a, 1], Subscript[a, 2], \[Ellipsis], Subscript[a, m + 1], -n}, {1 + Subscript[a, 1], 1 + Subscript[a, 2], \[Ellipsis], 1 + Subscript[a, m + 1]}, 1] (-(Gamma[Subscript[k, 0] - n]/Pi))^j (k - Subscript[k, 0])^m, {j, 0, m}], {m, 0, Infinity}] /; Subscript[a, 1] == Subscript[a, 2] == \[Ellipsis] == Subscript[a, m + 1] == Subscript[k, 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)





2007-05-02