       Re: Confluent hypergeometric functions of matrix argument

• To: mathgroup at smc.vnet.net
• Subject: [mg24577] Re: Confluent hypergeometric functions of matrix argument
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Tue, 25 Jul 2000 00:56:09 -0400 (EDT)
• Organization: Universitaet Leipzig
• References: <8lgt1n\$2eu@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

for a diagonal matrix you can just use the diagonal matrix
with the function values of the diagonal elements.
Because the definition is a power series D^n will be just

{{a,0,0},
{0,b,0},
{0,0,c}}^n will be {{a^n,0,0},
{0,b^n,0},
{0,0,c^n}}

Regards
Jens

Matthew Antone wrote:
>
> Hello,
>
> I'm looking for some code (preferably C, but FORTRAN or pseudocode for
> an algorithm would also be good) to compute the confluent hypergeometric
>
> function of matrix argument, 1F1(a; b; M).
>
> I only need to evaluate a specialized case, namely 1F1(0.5; 1.5; D)
> where D is a real diagonal 3x3 matrix. One of the diagonal elements of D
>
> is always 0, and the other two are arbitrary real values.
>
> I've seen various implementations of 1F1 for scalar arguments on netlib
> and other areas but I don't think they can be used for my problem.
>

```

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