Back to Search Start Over

Structural Formulas for Matrix-Valued Orthogonal Polynomials Related to 2×2 Hypergeometric Operators.

Authors :
Calderón, C.
Castro, M. M.
Source :
Bulletin of the Malaysian Mathematical Sciences Society. Mar2022, Vol. 45 Issue 2, p697-726. 30p.
Publication Year :
2022

Abstract

We give some structural formulas for the family of matrix-valued orthogonal polynomials of size 2 × 2 introduced by C. Calderón et al. in an earlier work, which are common eigenfunctions of a differential operator of hypergeometric type. Specifically, we give a Rodrigues formula that allows us to write this family of polynomials explicitly in terms of the classical Jacobi polynomials, and write, for the sequence of orthonormal polynomials, the three-term recurrence relation and the Christoffel–Darboux identity. We obtain a Pearson equation, which enables us to prove that the sequence of derivatives of the orthogonal polynomials is also orthogonal, and to compute a Rodrigues formula for these polynomials as well as a matrix-valued differential operator having these polynomials as eigenfunctions. We also describe the second-order differential operators of the algebra associated with the weight matrix. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
01266705
Volume :
45
Issue :
2
Database :
Academic Search Index
Journal :
Bulletin of the Malaysian Mathematical Sciences Society
Publication Type :
Academic Journal
Accession number :
155186118
Full Text :
https://doi.org/10.1007/s40840-021-01211-x