Moments of Askey-Wilson polynomials
Jang Soo Kim, Dennis Stanton
TL;DR
This paper introduces new formulas for the moments of Askey-Wilson polynomials, derived through analytic and combinatorial methods, and discusses related positivity properties and conjectures.
Contribution
It provides novel formulas for the moments of Askey-Wilson polynomials using analytic and combinatorial approaches, including Motzkin paths, matchings, and staircase tableaux.
Findings
New formulas for the nth moment of Askey-Wilson polynomials
A positivity theorem related to these moments
A conjecture on further positivity properties
Abstract
New formulas for the nth moment 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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