The search for differential equations for orthogonal polynomials by using computers
Roelof Koekoek

TL;DR
This paper develops a computer-aided method to find spectral differential equations for specific classes of orthogonal polynomials, extending previous work on Jacobi and Sobolev-Laguerre polynomials.
Contribution
It introduces a novel computer algebra approach to identify differential equations for orthogonal polynomials, enhancing analytical techniques in this area.
Findings
Preliminary differential equations for generalized Jacobi polynomials identified.
Differential equations for Sobolev-Laguerre polynomials explored.
Method demonstrates potential for automating spectral equation discovery.
Abstract
We look for spectral type differential equations for the generalized Jacobi polynomials found by T.H. Koornwinder in 1984 and for the Sobolev-Laguerre polynomials. We introduce a method which makes use of computeralgebra packages like Maple and Mathematica and we will give some preliminary results.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Mathematical functions and polynomials · Numerical methods for differential equations
