Some Properties of the Generalization of the p-Adic Factorial and the p-Adic Gamma Function

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Adıyaman Üniversitesi Fen Bilimleri Dergisi
Cilt: 15 Sayı: 1
Some Properties of the Generalization of the p-Adic Factorial and the p-Adic Gamma Function

Some Properties of the Generalization of the p-Adic Factorial and the p-Adic Gamma Function

Authors : Rafik Belhadef, Nour Elhouda Sahali

Pages : 128-145

Doi:10.37094/adyujsci.1543333

View : 37 | Download : 31

Publication Date : 2025-07-01

Article Type : Research Paper

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.
Keywords : Mahler expansions, p-adic gamma function, p-adic factorial, p-adic number

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