The Maxima on-line user's manual

Algebra Calculator

Binomial

Function: binomial (<x>, <y>) The binomial coefficient `<x>!/(<y>! (<x> - <y>)!)`. If <x> and <y> are integers, then the numerical value of the binomial coefficient is computed. If <y>, or <x - y>, is an integer, the binomial coefficient is expressed as a polynomial.

Examples:

```          (%i1) binomial (11, 7);
(%o1)                          330
(%i2) 11! / 7! / (11 - 7)!;
(%o2)                          330
(%i3) binomial (x, 7);
(x - 6) (x - 5) (x - 4) (x - 3) (x - 2) (x - 1) x
(%o3)   -------------------------------------------------
5040
(%i4) binomial (x + 7, x);
(x + 1) (x + 2) (x + 3) (x + 4) (x + 5) (x + 6) (x + 7)
(%o4) -------------------------------------------------------
5040
(%i5) binomial (11, y);
(%o5)                    binomial(11, y)```

There are also some inexact matches for `binomial`. Try `?? binomial` to see them.

```(%o1)                                true
(%i2) ```

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