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 RI moments coincide with orthogonal polynomial moments. The combinatorial results use weighted Motzkin paths, Schr\"oder paths, and parallelogram polyominoes.
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