Mathematics and Computational Sciences

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

Document Type : Original Article

Authors

D.L. Suthar 1, 2
Mulugeta Dawud Ali 3
Biniyam Shimelis 4

1 Department of Mathematics, College of Natural Science, Wollo University, Dessie, Ethiopia

2 Department of Mathematics, Saveetha School of Engineering (SIMATS), Thandalam 600124, Chennai, Tamil Nadu, India.

3 Department of Mathematics, College of Natural Science, Wollo university, Dessie, Ethiopia

4 Department of Mathematics, College of Natural Science, Wollo University, Dessie, Ethiopia.

https://doi.org/10.30511/mcs.2026.2068119.1434
Abstract
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.

Keywords

q-Fox's H-function
q-Riemann-Liouville derivative
q-Weyl derivative
q-Leibniz rule
Subjects
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Mathematics and Computational Sciences
Volume 7, Issue 3
Summer 2026
Pages 130-141

  • Receive Date 08 August 2025
  • Revise Date 02 June 2026
  • Accept Date 02 June 2026

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