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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