Expansion formulas for q-Hypergeometric and I q -functions: An application of the q-Leibniz rule

In this paper, we develop novel expansion formulas for the product of the basic analogue of the hypergeometric function and the Iq-function. Applying the q-Leibniz rule to the q-Riemann-Liouville and q-Weyl fractional derivative operators, we have found that these formulas can be derived more efficiently, potentially leading to new avenues of research within q-calculus and mathematical analysis. Furthermore, this study delves into specific cases of our main result, thereby elucidating the importance and utility of these derived expressions within a broader mathematical context.

کلیدواژه ها:

q-Fox's H-function ، q-Riemann-Liouville derivative ، q-Weyl derivative ، q-Leibniz rule