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Re: [Phys-L] Mathematics question

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

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?


Theorem 4.5 (Fuchs). Suppose the coefficients p(z) and q(z) of the second
order equation (4.20) have poles of order (at most) one and two respectively.
..............................................^^^^^^^


The "at most" is doing a lot of work in the statement of the theorem.
I think this is the proof you are looking for.
I haven't checked the details.

Gerald Teschl
_Ordinary Differential Equations and Dynamical Systems_

PDF downloadable from here:
https://www.mat.univie.ac.at/~gerald/ftp/book-ode/