       problem with DSolve and spheroidal harmonics

• To: mathgroup at smc.vnet.net
• Subject: [mg128292] problem with DSolve and spheroidal harmonics
• From: Tom Dickens <tomdickens at att.net>
• Date: Fri, 5 Oct 2012 02:49:27 -0400 (EDT)
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```All,

I wonder if this is a bug. I'm working on a project involving
spheroidal harmonics, and tried the following example from the Help:

DSolve[(1 - x^2) y''[x] -  2 x y'[x] + (SpheroidalEigenvalue[n, m, c]
+ c^2 (1 - x^2) - m^2-(  1 - x^2)) y[x] == 0, y, x]

{{y -> Function[{x},  C SpheroidalPS[n, m, c, x] + C
SpheroidalQS[n, m, c, x]]}}

This shows (in the Help) that the defining differential equation is
solved correctly. However, when I run it in either v7 or v8 I get a
differential root object

{{y->DifferentialRoot[Function[{-[FormalY],-[FormalX]},{-[FormalY][-[FormalX]]
(1--[FormalX]^2-c^2+-[FormalX]^2
c^2+m^2-SpheroidalEigenvalue[n,m,c])+2 -[FormalX]
(-[FormalY]^-[Prime])[-[FormalX]]+(-1+-[FormalX]^2)
(-[FormalY]^-[Prime]-[Prime])[-[FormalX]]==0,-[FormalY]==C,(-[FormalY]^-[Prime])==C}]]}}

Any thoughts?

Thanks,
Tom

```

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