Binomial coefficient

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(binomial coefficient, full definition, Matlab)
Current revision (20:08, 4 March 2022) (edit) (undo)
 
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Also see: [https://www.wolframalpha.com/input/?i=binomial+coefficient&assumption=%7B%22F%22%2C+%22BinomialCoefficientCalculator%22%2C+%22n%22%7D+-%3E%22-10%22&assumption=%7B%22F%22%2C+%22BinomialCoefficientCalculator%22%2C+%22k%22%7D+-%3E%225%22&assumption=%7B%22C%22%2C+%22binomial+coefficient%22%7D+-%3E+%7B%22Calculator%22%7D Wolfram <math>\alpha</math>]
Also see: [https://www.wolframalpha.com/input/?i=binomial+coefficient&assumption=%7B%22F%22%2C+%22BinomialCoefficientCalculator%22%2C+%22n%22%7D+-%3E%22-10%22&assumption=%7B%22F%22%2C+%22BinomialCoefficientCalculator%22%2C+%22k%22%7D+-%3E%225%22&assumption=%7B%22C%22%2C+%22binomial+coefficient%22%7D+-%3E+%7B%22Calculator%22%7D Wolfram <math>\alpha</math>]
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[[Image:Binomial.jpg|thumb|right|700px|full binomial coefficient definition including negative argument]]
<pre>
<pre>

Current revision

full definition, Matlab

binomial coefficient from M.J. Kronenburg [1]

Also see: Wolfram LaTeX: \alpha

full binomial coefficient definition including negative argument
full binomial coefficient definition including negative argument
function y = binomial(n, k)
if ~k || k == n
   y = 1;
elseif k == 1
   y = n;
elseif n < 0
   if k > 0
      y = (-1)^k*nchoosek(-n+k-1, k);
   elseif k <= n
      y = (-1)^(n-k)*nchoosek(-k-1, n-k);
   elseif n < k && k < 0
      y = 0;
   end
elseif n >= 0
   if k < 0 || k > n
      y = 0;
   else
      y = nchoosek(n,k);
   end
end
return
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