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.

Keywords

• askey-wilson polynomials
• moments of orthogonal polynomials
• motzkin paths
• hypergeometric series
• [info.info-dm]computer science [cs]/discrete mathematics [cs.dm]