# is it possible to extend combination C(n, k) definition to 2 real numbers C(r,s)?

Combination is defined as $C(n,k) = n! / k!(n-k)!$, where n & k are non-negative integers.

Now, the definition can be extend to C(r,k), where r is real number and k is an integer:

C(r,k) = r(r-1)...(r-k+1)/k! , where k>=0;
= 1 , where k = 0;
= 0 , where k < 0.


Question: is it possible to extend the definition even further, to be based on 2 real numbers, C(r,s), where both r and s are real numbers?

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Take a look at Beta function. – Tunococ Aug 30 '12 at 0:07
Possible duplicate of math.stackexchange.com/questions/188596/… In particular, Fly by Night's answer, and Tunococ's comment about the beta function provide an answer to this question. – Eric Naslund Aug 30 '12 at 1:53
I should note that extending definitions without a particular purpose in mind is maybe an amusing sport, but rather pointless in itself. And some day somebody might have a serious application that requires a different extension. – Marc van Leeuwen Aug 30 '12 at 5:08