Three families of q-Lommel polynomials

2021/05/21 by Jang Soo Kim, Kim, Jang Soo, Dennis Stanton +1 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2105.10096

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.

Cited by

• On q-real and q-complex numbers

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