Preprint Article Version 1 This version is not peer-reviewed

Some Relationships Including p-Adic Gamma Function and q-Daehee Polynomials and Numbers

Version 1 : Received: 19 February 2018 / Approved: 19 February 2018 / Online: 19 February 2018 (14:12:04 CET)

How to cite: Duran, U.; Acikgoz, M. Some Relationships Including p-Adic Gamma Function and q-Daehee Polynomials and Numbers. Preprints 2018, 2018020118 (doi: 10.20944/preprints201802.0118.v1). Duran, U.; Acikgoz, M. Some Relationships Including p-Adic Gamma Function and q-Daehee Polynomials and Numbers. Preprints 2018, 2018020118 (doi: 10.20944/preprints201802.0118.v1).

Abstract

In this paper, we investigate p-adic q-integral (q-Volkenborn integral) on Zp 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.

Subject Areas

p-adic numbers; p-adic gamma function; p-adic Euler constant; q-Daehee polynomials; Stirling numbers of the first kind

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