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Binomial






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Binomial[n,k] > Series representations > Asymptotic series expansions > Expansions at n==2k==infinity





http://functions.wolfram.com/06.03.06.0019.01









  


  










Input Form





Binomial[2 k, k] \[Proportional] (4^k/Sqrt[Pi k]) (1 - 1/(8 k) + 1/(128 k^2) + 5/(1024 k^3) - 21/(32768 k^4) + O[1/k^5]) /; (Abs[k] -> Infinity)










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