Bispectral Jacobi type polynomials
Classical Analysis and ODEs
2020-12-15 v1
Abstract
We study the bispectrality of Jacobi type polynomials, which are eigenfunctions of higher-order differential operators and can be defined by taking suitable linear combinations of a fixed number of consecutive Jacobi polynomials. Jacobi type polynomials include, as particular cases, the Krall-Jacobi polynomials. As the main results we prove that the Jacobi type polynomials always satisfy higher-order recurrence relations (i.e., they are bispectral). We also prove that the Krall-Jacobi families are the only Jacobi type polynomials which are orthogonal with respect to a measure on the real line.
Cite
@article{arxiv.2012.07618,
title = {Bispectral Jacobi type polynomials},
author = {Antonio J. Durán and Manuel D. de la Iglesia},
journal= {arXiv preprint arXiv:2012.07618},
year = {2020}
}
Comments
23 pages. arXiv admin note: text overlap with arXiv:1905.09223