Gaussian Hypergeometric Function

Computes gaussian hypergeometric function using a series expansion.

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

• MATLAB release: MATLAB 6.1 (R12.1)

[albert muthumalai]

 

[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.

[Hung tran]

thanh