An electrostatic model for the roots of discrete classical orthogonal polynomials

Joaquín F. Sánchez-Lara

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arXiv · 2410.10405

An electrostatic model for the roots of discrete classical orthogonal polynomials

Joaquín F. Sánchez-Lara

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Abstract

An electrostatic model is presented to describe the behaviour of the roots of classical discrete orthogonal polynomials. Indeed, this model applies in the more general frame of polynomial solutions of second-order linear difference equations $$A\Delta_h\nabla_h y+B\Delta_h y+ C y=0\,,$$ where $A$, $B$ and $C$ are polynomials and $$\Delta_h f(x)=f(x+h)-f(x)\qquad \text{ and }\qquad \nabla_h f(x)=f(x)-f(x-h)$$ with $h>0$.

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Joaquín F. Sánchez-Lara. 2024-10-14. An electrostatic model for the roots of discrete classical orthogonal polynomials. https://arxiv.org/abs/2410.10405

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