       Re: How to simplify?

• To: mathgroup at smc.vnet.net
• Subject: [mg96396] Re: [mg96161] How to simplify?
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Thu, 12 Feb 2009 06:43:40 -0500 (EST)

```\$Version

7.0 for Mac OS X x86 (64-bit) (November 11, 2008)

soln = y[r] /. DSolve[
y''[r] + 1/r y'[r] + y[r] == BesselJ[0, r],
y[r], r][] /. {C -> 0, C -> 0} //
FullSimplify

(r*BesselJ[1, r])/2

(1/4)*(Pi*r^2*(BesselJ[0, r]^2 +
BesselJ[1, r]^2)*BesselY[0, r] -
Sqrt[Pi]*BesselJ[0, r]*
MeijerG[{{3/2}, {1/2}}, {{1, 1}, {0, 1/2}}, r, 1/2]) //
FullSimplify

(r*BesselJ[1, r])/2

Version 7 expresses this specific MeijerG in terms of Bessel functions

MeijerG[{{3/2}, {1/2}}, {{1, 1}, {0, 1/2}}, r, 1/2]

Sqrt[Pi]*r^2*(BesselJ[0, r]*BesselY[0, r] + BesselJ[1, r]*BesselY[1, r])

Bob Hanlon

---- Aaron Fude <aaronfude at gmail.com> wrote:

=============
That's just not what I am getting.

DSolve[y''[r]+1/r
y'[r]+y[r]=C5 BesselJ[0,r],y[r],r][]/.{C(R)0,C(R)0}//FullSimplif=
y

{y[r](R)1/4 (p r2 (BesselJ[0,r]2+BesselJ[1,r]2) BesselY[0,r]- BesselJ[0,r]
MeijerG[{{3/2},{1/2}},{{1,1},{0,1/2}},r,1/2])}

I am using "6.0 for Microsoft Windows (32-bit) (May 21, 2008)"

Is the version the problem?

--

Bob Hanlon

```

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