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MathGroup Archive 2000

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Re: DSolve, it should be beautiful...

  • To: mathgroup at smc.vnet.net
  • Subject: [mg23286] Re: DSolve, it should be beautiful...
  • From: Hendrik van Hees <h.vanhees at gsi.de>
  • Date: Sun, 30 Apr 2000 21:13:36 -0400 (EDT)
  • Organization: GSI Darmstadt
  • References: <8eg7s6$hgc@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Nicola Attico wrote:
> 
> It seems to me that Mathematica DSolve is not able
> to find the solution of the very standard Legendre equation...
> 
> DSolve[(1-z^2) f''[z]-2 z f'[z]+(a(a+1)-(m^2/(1-z^2)))f[z]==0,f[z],z]
> 
I copied this expression to my Mathematica and got out

Out[2]//TextForm=
{{f[z] -> 
     C[1] LegendreP[
                               2
         -1 + Sqrt[1 + 4 (a + a )]        2
         -------------------------, Sqrt[m ], 
                     2
        z] + C[2] LegendreQ[
                               2
         -1 + Sqrt[1 + 4 (a + a )]        2
         -------------------------, Sqrt[m ], 
                     2
        z]}}

I have not checked wether this is correct but it looks good.

-- 
Hendrik van Hees		Phone:  ++49 6159 71-2751
c/o GSI-Darmstadt SB3 3.183	Fax:    ++49 6159 71-2990
Planckstr. 1			mailto:h.vanhees at gsi.de
D-64291 Darmstadt		http://theory.gsi.de/~vanhees/index.html


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