Duran, U.; Acikgoz, M. A Study on Novel Extensions for the p-adic Gamma and p-adic Beta Functions. Math. Comput. Appl. 2019, 24, 53.
Duran, U.; Acikgoz, M. A Study on Novel Extensions for the p-adic Gamma and p-adic Beta Functions. Math. Comput. Appl. 2019, 24, 53.
Duran, U.; Acikgoz, M. A Study on Novel Extensions for the p-adic Gamma and p-adic Beta Functions. Math. Comput. Appl. 2019, 24, 53.
Duran, U.; Acikgoz, M. A Study on Novel Extensions for the p-adic Gamma and p-adic Beta Functions. Math. Comput. Appl. 2019, 24, 53.
Abstract
In this paper, we introduce the (ρ,q)-analogue of the p-adic factorial function. By utilizing some properties of (ρ,q)-numbers, we obtain several new and interesting identities and formulas. We then construct the p-adic (ρ,q)-gamma function by means of the mentioned factorial function. We investigate several properties and relationships belonging to the foregoing gamma function, some of which are given for the case p = 2. We also derive more representations of the p-adic (ρ,q)-gamma function in general case. Moreover, we consider the p-adic (ρ,q)-Euler constant derived from the derivation of p-adic (ρ,q)-gamma function at x = 1. Furthermore, we provide a limit representation of aforementioned Euler constant based on (ρ,q)-numbers. Finally, we consider (ρ,q)-extension of the p-adic beta function via the p-adic (ρ,q)-gamma function and we then investigate various formulas and identities.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Ugur Duran
Mehmet Acikgoz