Abstract
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) |
|---|---|
| Pages (from-to) | 169-180 |
| 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 note
Funding 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 .
Keywords
- Askey-wilson polynomials
- Hypergeometric series
- Moments of orthogonal polynomials
- Motzkin paths