Symmetry of terminating series representations of the Askey-Wilson polynomials
| Autor: | Cohl, Howard S., Costas-Santos, Roberto S. |
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| Rok vydání: | 2022 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 ${}_4\phi_3$ and terminating very-well poised ${}_8W_7$ 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 $S_6$, the symmetry group of the terminating balanced ${}_4\phi_3$. We then use terminating balanced ${}_4\phi_3$ and terminating very-well poised ${}_8W_7$ transformations to give a broader interpretation of Watson's $q$-analog of Whipple's theorem and its converse. We give a broad description of the symmetry structure of the terminating basic hypergeometric series representations of the Askey--Wilson polynomials. Comment: arXiv admin note: text overlap with arXiv:2006.14021 |
| Databáze: | arXiv |
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