1
$\begingroup$

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?

  • 0
    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.2012-08-30

0 Answers 0