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MathGroup Archive 2000

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Re: Confluent hypergeometric function of matrix argument

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24592] Re: Confluent hypergeometric function of matrix argument
  • From: Roland Franzius <Roland.Franzius at uos.de>
  • Date: Tue, 25 Jul 2000 00:56:24 -0400 (EDT)
  • References: <8lgu6j$2j8@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

If your matrix power means matrix product,
for a diagonal matrix simply map the function into the matrix:  
1F1[ { (0,0,0),(0,a,0),(0,0,b)} ] ={ (0,0,0),(0,1F1(a),0),(0,0,1F1(b) } 
Of course you can save time using only the diagonal vector and use
multiplication like scalar product without sum

(a,b,c) * (A,B,C) =(a*A,b*B,c*C) 

Matt Antone wrote:
> 
> 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.

-- 
Roland Franzius

  +++ exactly <<n>> lines of this message have value <<FALSE>> +++


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