@article{article_1543333, title={Some Properties of the Generalization of the p-Adic Factorial and the p-Adic Gamma Function}, journal={Adıyaman University Journal of Science}, volume={15}, pages={128–145}, year={2025}, DOI={10.37094/adyujsci.1543333}, author={Belhadef, Rafik and Sahali, Nour Elhouda}, keywords={Mahler expansions, p-adic gamma function, p-adic factorial, p-adic number}, abstract={In this paper, we introduce the concept of q-adic factorial, establishing several significant congruences and inequalities associated with this new function. For a good illustration, we provide some numerical examples. Furthermore, we prove several properties of the generalized p-adic gamma function Γ_q, along with identities and special values related to Γ_q. We also derive a representation of Γ_q via its Mahler expansion and establish relationships among the coefficients within this expansion.}, number={1}, publisher={Adıyaman Üniversitesi}, organization={Laboratory of Pure and Applied Mathematics, University of Jijel}