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arXiv · 2608.28414

A unified approach via Geronimus transformation to various types of orthogonal polynomials

Maxim Derevyagin·Juan Carlos García Ardila
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Abstract

We present a unified Geronimus-type construction that leads to various orthogonal polynomials including indefinite orthogonal polynomials, exceptional and, more generally, lacunary orthogonal polynomials, and multiple orthogonal polynomials. We use generalized Hermite polynomials to demonstrate the idea and obtain various results for the Geronimus-type transformation such as zero location, recurrence relations, and differential equations.

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Maxim Derevyagin, Juan Carlos García Ardila. 2026-08-28. A unified approach via Geronimus transformation to various types of orthogonal polynomials. https://arxiv.org/abs/2608.28414

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