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MathGroup Archive 2005

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Re: MeijerG again

  • To: mathgroup at smc.vnet.net
  • Subject: [mg55705] Re: [mg55688] MeijerG again
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Mon, 4 Apr 2005 00:59:11 -0400 (EDT)
  • Reply-to: hanlonr at cox.net
  • Sender: owner-wri-mathgroup at wolfram.com

$Version

5.1 for Mac OS X (January 27, 2005)

Clear[f,x,t];
f[t_] = FullSimplify[f[t] /.DSolve[
          {Sin[t]*f''[t]+Cos[t]*f'[t]+3/4*Sin[t]*f[t]==0,
            f[-Pi/2]==1, f'[-Pi/2]==0},f[t],t][[1]]]

(8*Sqrt[Pi]*(Pi*LegendreP[1/2, Cos[t]]*LegendreQ[-(1/2), 0] - 
    2*EllipticK[1/2]*LegendreQ[1/2, Cos[t]]))/
  (8*Pi^(3/2) + EllipticK[1/2]*Gamma[-(1/4)]^2)

{f[-Pi/2]//FullSimplify,f'[-Pi/2]}

{1,0}


Bob Hanlon

> 
> From: "Zakir F. Seidov" <seidov at bgumail.bgu.ac.il>
To: mathgroup at smc.vnet.net
> Date: 2005/04/03 Sun AM 05:50:56 EDT
> To: mathgroup at smc.vnet.net
> Subject: [mg55705] [mg55688] MeijerG again
> 
> Dear Mathematica gurus!
> I need to solve (a rather simple?) ODE:
> DSolve[{Sin[t]*f''[t]+Cos[t]*f'[t]+3/4*Sin[t]*f[t]== 
> 0}, f[t], t] 
> Mathematica 4 gives:
> {{f[t] ->C[1]*Hypergeometric2F1[-(1/4), 3/4, 1, Sin[t]^2] 
+C[2]*MeijerG[{{},{1/4, 5/4}},{{0, 0},{}},Sin[t]^2]}}
> It's OK, but I need initial conditions: f[-Pi/2]=1 and f'[-Pi/2]=0.
> Mathematica 4 refuses to find C[1] and C[2].
> Pleeeese HHHEEELLLPPP!!!
> 
> 


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