An algebraic treatment of the Pastro polynomials on the real line

Chea, Vutha Vichhea; Vinet, Luc; Zaimi, Meri; Zhedanov, Alexei

doi:10.1090/proc/16458

An algebraic treatment of the Pastro polynomials on the real line
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by Vutha Vichhea Chea, Luc Vinet, Meri Zaimi and Alexei Zhedanov

Proc. Amer. Math. Soc. 151 (2023), 4405-4418

DOI: https://doi.org/10.1090/proc/16458

Published electronically: May 25, 2023

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Abstract:

The properties of the Pastro polynomials on the real line are studied with the help of a triplet of $q$-difference operators. The $q$-difference equation and recurrence relation these polynomials obey are shown to arise as generalized eigenvalue problems involving the triplet of operators, with the Pastro polynomials as solutions. Moreover, a discrete biorthogonality relation on the real line for the Pastro polynomials is obtained and is then understood using adjoint operators. The algebra realized by the triplet of $q$-difference operators is investigated.

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