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

An algebraic treatment of the Pastro polynomials on the real line. (English) Zbl 1539.39004

Proc. Am. Math. Soc. 151, No. 10, 4405-4418 (2023).
The authors study properties of Pastro polynomials on the real line, by introducing three \(q\)-difference operators that play a role similar to the pair of bispectral operators of the classical orthogonal polynomials, but for biorthogonal polynomials instead. The Pastro polynomials then arise as the polynomial solutions of generalized eigenvalue problems that are generated by these operators, which yields a description of their bispectral properties. As a result, the authors obtain a discrete biorthogonality relation on the real line for the Pastro polynomials.
Reviewer: Christoph Koutschan (Linz)

MSC:

39A13 Difference equations, scaling (\(q\)-differences)
39A70 Difference operators
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)
47B36 Jacobi (tridiagonal) operators (matrices) and generalizations
05A30 \(q\)-calculus and related topics

Keywords:

Pastro polynomials; discrete biorthogonality relation; \(q\)-difference equation; \(q\)-difference operators
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References:

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