Binomial

R←X!Y

X and Y may be any numbers except that if Y is a negative integer then X must be a whole number (integer). R is numeric. An element of R is integer if corresponding elements of X and Y are integers. Binomial is defined in terms of the function Factorial for positive integer arguments:

      X!Y ←→ (!Y)÷(!X)×!Y-X

For other arguments, results are derived smoothly from the Beta function:

      Beta(X,Y) ←→ ÷Y×(X-1)!X+Y-1

For positive integer arguments, R is the number of selections of X things from Y things.

Example

      1 1.2 1.4 1.6 1.8 2!5
5 6.105689248 7.219424686 8.281104786 9.227916704 10
 
      2!3j2
1J5