Interesting deformed q-series involving the central Lucasnomial coefficients

Abstract

In this paper, we derive a variety of interesting q-series that contain central Lucasnomial coefficients. Our approach is based on manipulating deformed basic hypergeometric series. Deformed q-analogues of the Euler, Rogers–Ramanujan, and Exton types are obtained. Additionally, we derive some generating functions of the Lucas-analogue of Catalan numbers.