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Re: Two questions about DSolve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg93095] Re: Two questions about DSolve
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Sun, 26 Oct 2008 01:27:45 -0500 (EST)
  • References: <gdug9e$jon$1@smc.vnet.net>

Hi,

I get

{y[r] -> BesselY[m, r]*C[2] + (r^(2*m)*BesselJ[-m, r]*Gamma[-m]*
      HypergeometricPFQ[{m, 1/2 + m}, {1 + m, 1 + m, 1 + 2*m},
       -r^2])/(2^(2*(1 + m))*m^2*Gamma[m]) -
    (Pi*r^2*BesselJ[m, r]*Csc[m*Pi]*HypergeometricPFQRegularized[
       {1, 1, 3/2}, {2, 2, 2 - m, 2 + m}, -r^2])/8 +
    BesselJ[m, r]*(C[1] + Log[r]/(2*m))}

with Mathematica 6 -- an there i  no MeijerG[] in it.
And no, Mathematica can't know what m is and that you
you wish to take the limit r->0

Regards
   Jens

Aaron Fude wrote:
> Hi,
> 
> My goal is to solve
> 
> DSolve[r^2 y''[r] + r y'[r] + (r^2 - m^2) y[r] == BesselJ[m, r],
> y[r],  r]
> 
> Question 1. Is there a way to tell Mathematica that I want the
> solutions that are finite at r=0?
> 
> Question 2. I get answers in terms of MeijerG. How does one obtain the
> special form of this function from the special combination of
> arguments. For example, I'm would like to learn what function
> 
> MeijerG[{{1/2}, {-(1/2), 1}}, {{0, 0, 0}, {-(1/2), 0}}, r, 1/2]
> 
> is in terms of more elementary functions.
> 
> Many thanks in advance,
> 
> Aaron
> 


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