Question about Orthogonal Polynomials

[facenian]

Hello, I'm studing the hydrogen atom and I found an unified presentation of orhtogonal polynomials in the book by Fuller and Byron. I would like to learn more about it but in the same spirit(for physicits not for mathematicians). Can someone give some references where to find more?

 

[dextercioby]

Hmm, for physics usually a book like Byron-Fuller / Arfken / Morse & Feshbach would do. However, when you see the subject from the mathematical perspective, you can go deeper, into Hilbert space theory or into the analysis of hypergeometric functions which are the most natural generalizations.

 

[VortexLattice]

What do you mean, like Hermite polynomials? Bessel functions are also basically polynomials. And of course Legendre polynomials. I'd learn those, we use all those in QM.

 

[facenian]

Arfken and Fuller presents clearly like a problem of eingenvalues of a selfadoint operator(sturn Liouville system) then he analyzes the conditions for the equation to render polynomials solution and from this one obteins all polynomials solutions(Hermite,Legendre,Laguerre,etc.) in a single framework and not like separate cases, for instance one can obtein a general Rodrigues formula encompassing all cases. It is very interesting and all done without fancy mathematics. I would very much like to see more of this, I mean more details, expleined by another author to complement the excellent presentation of Fuller/Byron