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Re: problem with DSolve and spheroidal harmonics

• To: mathgroup at smc.vnet.net
• Subject: [mg128309] Re: problem with DSolve and spheroidal harmonics
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Sat, 6 Oct 2012 01:49:32 -0400 (EDT)
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• References: <20121005064927.8A81F6863@smc.vnet.net>

$Version

"8.0 for Mac OS X x86 (64-bit) (October 5, 2011)"

You entered  m^2-(1-x^2)  rather than  m^2/(1-x^2)

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[1] SpheroidalPS[n, m, c, x] + C[2] SpheroidalQS[n, m, c, x]]}}


Bob Hanlon


On Fri, Oct 5, 2012 at 2:49 AM, Tom Dickens <tomdickens at att.net> wrote:
> 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[1] SpheroidalPS[n, m, c, x] + C[2]
> 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][0]==C[1],(-[FormalY]^-[Prime])[0]==C[2]}]]}}
>
> Any thoughts?
>
> Thanks,
> Tom
>

• References:
  • problem with DSolve and spheroidal harmonics
    • From: Tom Dickens <tomdickens@att.net>