Efficient Computation involving a Hypergeometric function...

*To*: mathgroup at smc.vnet.net*Subject*: [mg72584] Efficient Computation involving a Hypergeometric function...*From*: "Richard Palmer" <rhpalmer at gmail.com>*Date*: Wed, 10 Jan 2007 03:23:08 -0500 (EST)

I have a discrete distribution: \!\(f\ \ = \ \ Binomial[x + n, x]\ p\^\(x + 1\)\ \((1 - p)\)\^n\) Here p and x are fixed, p is real between 0 and 1, x and n are integers greater than or equal to zero, and n is the parameter (n,0,Infinity). The CDF is \!\(1 - \(\((1 - p)\)\^\(1 + n\)\ p\^\(1 + x\)\ Ã[2 + n + x]\ \ Hypergeometric2F1Regularized[1, 2 + n + x, 2 + n, 1 - p]\)\/Ã[1 + x]\) where n is actually Floor[n]. Does anybody see a simplification or asymtotic for the CDF that provides an efficient way to compute this for large n (say n ge 1000)? I need to solve CDF==k for various fixed p and x. Thanks in advance! -- Richard Palmer