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 >