Negative binomial series

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

Description

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)

• MATLAB release: MATLAB 7 (R14)