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arXiv · 2307.15415

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

Edmundo J. Huertas·Alberto Lastra·Víctor Soto-Larrosa
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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

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Edmundo J. Huertas, Alberto Lastra, Víctor Soto-Larrosa. 2023-07-28. On a moment generalization of some classical second-order differential equations generating classical orthogonal polynomials. https://arxiv.org/abs/2307.15415

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