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.
|Original language||English (US)|
|Number of pages||12|
|Journal||Discrete Mathematics and Theoretical Computer Science|
|State||Published - 2013|
|Event||25th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2013 - Paris, France|
Duration: Jun 24 2013 → Jun 28 2013
Bibliographical noteFunding Information:
The first author was partially supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( NRF-2013R1A1A2061006 ). The second author was supported by NSF Grant DMS-1148634 .
Copyright 2013 Elsevier B.V., All rights reserved.
- Askey-wilson polynomials
- Hypergeometric series
- Moments of orthogonal polynomials
- Motzkin paths