Jang Soo Kim ; Dennis Stanton - Moments of Askey-Wilson polynomials

dmtcs:12802 - Discrete Mathematics & Theoretical Computer Science, January 1, 2013, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) - https://doi.org/10.46298/dmtcs.12802
Moments of Askey-Wilson polynomialsArticle

Authors: Jang Soo Kim 1; Dennis Stanton 1

  • 1 School of Mathematics

New formulas for the $n^{\mathrm{th}}$ moment $\mu_n(a,b,c,d;q)$ of the Askey-Wilson polynomials are given. These are derived using analytic techniques, and by considering three combinatorial models for the moments: Motzkin paths, matchings, and staircase tableaux. A related positivity theorem is given and another one is conjectured.


Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: Askey-Wilson polynomials,moments of orthogonal polynomials,Motzkin paths,hypergeometric series,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]

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