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### Highlights from Gaussian Hypergeometric Function

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# Gaussian Hypergeometric Function

### Diego Garcia (view profile)

17 Jun 2002 (Updated )

Computes gaussian hypergeometric function using a series expansion.

File Information
Description

HYPERGEOMETRIC2F1 Computes a hypergeometric function using the series expansion:

f(a,b;c;x)=
1 + [ab/1!c]x + [a(a+1)b(b+1)/2!c(c+1)]x^2 +[a(a+1)(a+2)b(b+1)(b+2)/3!c(c+1)(c+2)]x^3 + ...

This function solves the Gaussian Hypergeometric Differential Equation:

x(1-x)y'' + {c-(a+b+1)x}y' - aby = 0

Acknowledgements

This file inspired Generation Of Random Variates.

MATLAB release MATLAB 6.1 (R12.1)
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Comments and Ratings (4)
05 Apr 2012 David Holdaway

### David Holdaway (view profile)

It's pretty good if you want to calculate the Hypergeometric series for values at which it terminates after a finite number of terms. If you want non finite series (which is usually the case) this will converge slowly, needs patching with methods for large x etc.

08 Feb 2007 Hung tran

thanh

Comment only
04 Feb 2004 Bryan Reed

Does a good job at small x, but by the way it's calculated is useless as x gets close to 1. Should switch to a different functional form for arguments in the upper half of the range. Would be more efficient and trustworthy, also, if it automatically determined when to truncate the series to get the desired accuracy.

01 Oct 2003 albert muthumalai