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Binomial




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Binomial[n,k] > Series representations > Generalized power series > Expansions at generic point n==n0 > For the function itself





http://functions.wolfram.com/06.03.06.0008.01









  


  








Input Form





Binomial[n, k] \[Proportional] Binomial[Subscript[n, 0], k] (1 + (HarmonicNumber[Subscript[n, 0]] - HarmonicNumber[ -k + Subscript[n, 0]]) (n - Subscript[n, 0]) + (1/2) ((HarmonicNumber[Subscript[n, 0]] - HarmonicNumber[ -k + Subscript[n, 0]])^2 + PolyGamma[1, 1 + Subscript[n, 0]] - PolyGamma[1, 1 - k + Subscript[n, 0]]) (n - Subscript[n, 0])^2 + \[Ellipsis]) /; (n -> Subscript[n, 0]) && !(Element[k, Integers] && k > 0)








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