Negative binomial series

binomial,negative binomal,Newton's binomial,binomial theorem

This m-file gives the expansion of powers of sums of any real or complex numbers x and y, and any negative integer n. In 1676 Newton showed that the binomial theorem also holds for negative integers n, which is the so-called negative binomial series and converges for |x| < y. From this emerges the negative binomial distribution, a discrete probability distribution.

Syntax: function negbins(x,y,n)

Input:
x,y - pair of interested terms to expand
n - coefficient/power to increase the binomial theorem (it is
a negative integer that file automatically gives)

Output:
- result of the negative binomial series sum
- vector of the negative binomial series (optional)