| Title | Symmetry of terminating basic hypergeometric series representations of the Askey–Wilson polynomials |
|---|---|
| Authors | Cohl H.S. , COSTAS SANTOS, ROBERTO SANTIAGO |
| External publication | No |
| Means | J. Math. Anal. Appl. |
| Scope | Article |
| Nature | Científica |
| JCR Quartile | 1 |
| SJR Quartile | 1 |
| JCR Impact | 1.2 |
| SJR Impact | 0.816 |
| Publication date | 01/01/2023 |
| ISI | 000859426700003 |
| Scopus Id | 2-s2.0-85144034862 |
| DOI | 10.1016/j.jmaa.2022.126583 |
| Abstract | In this paper, we explore the symmetric nature of the terminating basic hypergeometric series representations of the Askey–Wilson polynomials and the corresponding terminating basic hypergeometric transformations that these polynomials satisfy. In particular we identify and classify the set of 4 and 7 equivalence classes of terminating balanced ?34 and terminating very-well-poised W78 basic hypergeometric series which are connected with the Askey–Wilson polynomials. We study the inversion properties of these equivalence classes and also identify the connection of both sets of equivalence classes with the symmetric group S6, the symmetry group of the terminating balanced ?34. We then use terminating balanced ?34 and terminating very-well poised W78 transformations to give a broader interpretation of Watson\'s q-analog of Whipple\'s theorem and its converse. © 2022 |
| Keywords | Basic hypergeometric orthogonal polynomials; Basic hypergeometric series; Basic hypergeometric transformations |
| Universidad Loyola members |