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Confluent hypergeometric function of matrix argument

• To: mathgroup at smc.vnet.net
• Subject: [mg24564] Confluent hypergeometric function of matrix argument
• From: "Matt Antone" <tone at MIT.EDU>
• Date: Mon, 24 Jul 2000 03:04:48 -0400 (EDT)
• Organization: MIT Laboratory for Computer Science
• Sender: owner-wri-mathgroup at wolfram.com

Hello,

I'm looking for some code (preferably C, but FORTRAN or pseudocode for an
algorithm would also be fine) to compute the confluent hypergeometric
function of matrix argument, 1F1(a; b; M).

I only need to evaluate for a couple of specific cases:

1F1(0.5; 1.5; D) where D is a real 3x3 diagonal matrix with one diagonal
entry = 0, and

1F1(0.5; 2; D) where D is a real 4x4 diagonal matrix with one diagonal entry
= 0.

I've seen various implementations of the function of scalar arguments on
netlib and in other areas but I don't think they can be used in this case.
Ideally I'd like code to compute the above values of 1F1, or the logarithm
of these values, and also take first and second derivatives with respect to
the matrix parameters in D.

Any help would be greatly appreciated. Please respond to tone at mit.edu and/or
post to this group if you have any leads.

Thanks in advance,