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# Re: [Phys-L] Mathematics question

Fuchs's theorem guarantees that at least one power series solution will be obtained when applying the Frobenius method if the expansion point is an ordinary, or regular, singular point. For a regular singular point, a Laurent series expansion can also be used.   [https://mathworld.wolfram.com/FrobeniusMethod.html]

Fuchs seems to be the only copper-bottomed proof concerning Frobenius - and this regular singular point requirement  is something you [Peter Schoch] already know]
On Wednesday, May 12, 2021, 09:36:02 PM CDT, John Denker via Phys-l <phys-l@mail.phys-l.org> wrote:

On 5/12/21 5:53 PM, Peter Schoch wrote:

Do any of you know of a proof that shows the
Method of Frobenius could be used for anything other than just "regular
singular point" problems?

You can find more information by googling for "Fuchsian".

https://en.wikipedia.org/wiki/Lazarus_Fuchs
https://en.wikipedia.org/wiki/Fuchs%27_theorem

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Kudos to the student. It's a really great question.

Kudos to PS for encouraging students to ask such questions.
It means they are /thinking/ about the material.

If the kid ever asks for a letter of recommendation, be sure
to mention this. Many of the letters are alike and/or hard to
evaluate, but this is the sort of thing that really stands out.
It grabs the attention of the folks who read such letters.
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