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 --