New formulas for the nth moment μn(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.
- Askey-Wilson polynomials
- Moments of orthogonal polynomials
- Motzkin paths
- Staircase tableaux