Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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?

share|improve this question
1  
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

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.