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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.38 no.4 Antofagasta dic. 2019

http://dx.doi.org/10.22199/issn.0717-6279-2019-04-0052 

Articles

On p-adic gamma function related to q-Daehee polynomials and numbers

1Iskenderun Technical University, Dept. of the Basic Concepts of Engineering, Iskenderun, Turkey, e-mail : ugur.duran@iste.edu.tr

2University of Gaziantep, Dept. of Mathematics, Gaziantep, Turkey, e-mail: acikgoz@gantep.edu.tr

Abstract

In this paper, we investigate p-adic q-integral (q-Volkenborn integral) on Z p of p-adic gamma function via their Mahler expansions. We also derived two q-Volkenborn integrals of p-adic gamma function in terms of q-Daehee polynomials and numbers and q-Daehee polynomials and numbers of the second kind. Moreover, we discover q-Volkenborn integral of the derivative of p-adic gamma function. We acquire the relationship between the p-adic gamma function and Stirling numbers of the first kind. We finally develop a novel and interesting representation for the p-adic Euler constant by means of the q-Daehee polynomials and numbers.

Keywords: p-adic numbers, p-adic gamma function; p-adic Euler constant; Mahler expansion; q-Daehee polynomials; Stirling numbers of the first kind.

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Received: August 2018; Accepted: September 2018

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