English

On a moment generalization of some classical second-order differential equations generating classical orthogonal polynomials

Classical Analysis and ODEs 2023-07-31 v1

Abstract

The aim of the work is to construct new polynomial systems, which are solutions to certain functional equations which generalize the second-order differential equations satisfied by the so called classical orthogonal polynomial families of Jacobi, Laguerre, Hermite and Bessel. These functional equations can be chosen to be of different type: fractional differential equations, q-difference equations, etc, which converge to their respective differential equations of the aforesaid classical orthogonal polynomials. In addition to this, there exists a confluence of both the families of polynomials constructed and the functional equations who approach to the classical families of polynomials and second-order differential equations, respectively

Keywords

Cite

@article{arxiv.2307.15415,
  title  = {On a moment generalization of some classical second-order differential equations generating classical orthogonal polynomials},
  author = {Edmundo J. Huertas and Alberto Lastra and Víctor Soto-Larrosa},
  journal= {arXiv preprint arXiv:2307.15415},
  year   = {2023}
}
R2 v1 2026-06-28T11:42:41.604Z