The Cauchy Operator for Basic Hypergeometric Series
| dc.creator | Chen, Vincent Y. B. | |
| dc.creator | Gu, Nancy S. S. | |
| dc.date | 2007-05-13 | |
| dc.date | 2007-08-21 | |
| dc.date.accessioned | 2026-07-07T08:24:12Z | |
| dc.date.available | 2026-07-07T08:24:12Z | |
| dc.description | We introduce the Cauchy augmentation operator for basic hypergeometric series. Heine's ${}_2ϕ_1$ transformation formula and Sears' ${}_3ϕ_2$ transformation formula can be easily obtained by the symmetric property of some parameters in operator identities. The Cauchy operator involves two parameters, and it can be considered as a generalization of the operator $T(bD_q)$. Using this operator, we obtain extensions of the Askey-Wilson integral, the Askey-Roy integral, Sears' two-term summation formula, as well as the $q$-analogues of Barnes' lemmas. Finally, we find that the Cauchy operator is also suitable for the study of the bivariate Rogers-Szegö polynomials, or the continuous big $q$-Hermite polynomials. | |
| dc.description | 21 pages, to appear in Advances in Applied Mathematics | |
| dc.identifier | https://arxiv.org/abs/0705.1812 | |
| dc.identifier | http://arxiv.org/abs/0705.1812 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/136263 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A30, 33D05, 33D15 | |
| dc.title | The Cauchy Operator for Basic Hypergeometric Series | |
| dc.type | text |