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MathGroup Archive 2000

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Re: hating DSolve...

  • To: mathgroup at smc.vnet.net
  • Subject: [mg23281] Re: [mg23273] hating DSolve...
  • From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
  • Date: Sun, 30 Apr 2000 21:13:33 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

on 00.4.30 11:05 AM, Nicola Attico at attico at localhost.localdomain wrote:

> It seems to me that Mathematica DSolve is not able
> to find the solution of the very standard Legendre equation...
> When it could be useful....
> 
> DSolve[(1-z^2) f''[z]-2 z f'[z]+(a(a+1)-(m^2/(1-z^2)))f[z]==0,f[z],z]
> 
> 
> Nicola Attico
> 
> 

Your message seems to me rather strange. Indeed, you are right that
Mathematica 3.0 can't do the above:

DSolve[(1 - z^2) f''[z] - 2 z f'[z] + (a(a + 1) - (m^2/(1 - z^2)))f[z] == 0,
  f[z], z]

                       2
                      m
DSolve[(a (1 + a) - ------) f[z] - 2 z f'[z] +
                         2
                    1 - z
 
          2
    (1 - z ) f''[z] == 0, f[z], z]

So, you would have been right to complain a year or so ago. But in
Mathematica 4.0 you get:

DSolve[(1 - z^2) f''[z] - 2 z f'[z] + (a(a + 1) - (m^2/(1 - z^2)))f[z] == 0,
  f[z], z]

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

This looks right.

Best regards

Andrzej Kozlowski
--




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