Three families of $q$-Lommel polynomials

Abstract

Three $q$-versions of Lommel polynomials are studied. Included are explicit representations, recurrences, continued fractions, and connections to associated Askey--Wilson polynomials. Combinatorial results are emphasized, including a general theorem when $R_I$ moments coincide with orthogonal polynomial moments. The combinatorial results use weighted Motzkin paths, Schröder paths, and parallelogram polyominoes.

24 pages, 4 figures

References in corpus (1)

• Ratios of Hahn--Exton $q$-Bessel functions and $q$-Lommel polynomials