Re: Appell Hypergeometric Function

In article <1168899529.177303.316390@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"user923005" <dcorbit@xxxxxxxxx> wrote:

OliveWork@xxxxxxxxx wrote:
I'm doing numerical evaluation of second kind Appell Hypergeometric
Function with two variables.

Reference link:
http://mathworld.wolfram.com/AppellHypergeometricFunction.html

First kind Appell Hypergeometric Function with two variables is
implemented as AppellF1.

Is there any implementation of second kind Appell Hypergeometric
Function with two variables in any math software package? The brute
force implementation in Matlab often overflows.

Thanks for your input!

This looks useful and relevant:
"Geometry and arithmetic associated to Appell hypergeometric partial
differential equations"
Authors:, Yang, Lei

If you only need a few accurate answers, I would use the definition for
equation 5 found here:
http://mathworld.wolfram.com/AppellHypergeometricFunction.html

Actually, equation 5 is _not_ a definition of AppellF2. At this URL it
says that Appell defined the functions in 1880, and Picard showed in
1881 that they may all be expressed by integrals of the form (5), and
gives the reference (Bailey 1934, pp. 76-79). Referring to the Bailey
reference, one does not find an integral of the form (5), but one does
find a definition involving a double integral. See

http://physics.uwa.edu.au/pub/Mathematica/MathGroup/AppellF.nb

if you have access to Mathematica and

http://physics.uwa.edu.au/pub/Mathematica/MathGroup/AppellF.pdf

if not.

If you only need a few accurate answers, I would use Mathematica.

Cheers,
Paul

_______________________________________________________________________
Paul Abbott Phone: 61 8 6488 2734
School of Physics, M013 Fax: +61 8 6488 1014
The University of Western Australia (CRICOS Provider No 00126G)
AUSTRALIA http://physics.uwa.edu.au/~paul
.