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Moments of Askey-Wilson polynomials

Abstract : 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.
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https://hal.inria.fr/hal-01229707
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Jang Soo Kim, Dennis Stanton. Moments of Askey-Wilson polynomials. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. pp.169-180. ⟨hal-01229707⟩

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