Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

On p-adic Gamma Function Related to q-Daehee Polynomials and Numbers

Version 1 : Received: 15 May 2019 / Approved: 16 May 2019 / Online: 16 May 2019 (15:33:45 CEST)

How to cite: Duran, U.; Acikgoz, M. On p-adic Gamma Function Related to q-Daehee Polynomials and Numbers. Preprints 2019, 2019050215. https://doi.org/10.20944/preprints201905.0215.v1 Duran, U.; Acikgoz, M. On p-adic Gamma Function Related to q-Daehee Polynomials and Numbers. Preprints 2019, 2019050215. https://doi.org/10.20944/preprints201905.0215.v1

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.

Subject

Computer Science and Mathematics, Algebra and Number Theory

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