PreprintCC BY-NC-ND 4.0arXiv
A unified approach via Geronimus transformation to various types of orthogonal polynomials
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.
Related
- An Exploration of Lacunary Orthogonal Polynomials Associated with the Geronimus Transformation
- Matrix orthogonal polynomials related to diffference operators for L-orthogonal polynomials
- Identities and congruences involving orthogonal polynomials and Apéry-like numbers
- Time-and-band limiting for symmetric classical Dunkl orthogonal polynomials
- Piñeiro mixed orthogonal polynomials and bidiagonal factorization
BibTeX
@misc{derevyagin2026unified,
title = {{A unified approach via Geronimus transformation to various types of orthogonal polynomials}},
author = {Maxim Derevyagin and Juan Carlos García Ardila},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28414},
eprint = {2608.28414},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28414},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - A unified approach via Geronimus transformation to various types of orthogonal polynomials
AU - Maxim Derevyagin
AU - Juan Carlos García Ardila
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.28414
UR - https://arxiv.org/abs/2608.28414
AB - 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.
ER -