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. Preprints2018, 2018020118. https://doi.org/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. https://doi.org/10.20944/preprints201802.0118.v1
Duran, U.; Acikgoz, M. Some Relationships Including p-Adic Gamma Function and q-Daehee Polynomials and Numbers. Preprints2018, 2018020118. https://doi.org/10.20944/preprints201802.0118.v1
APA Style
Duran, U., & Acikgoz, M. (2018). Some Relationships Including <em>p</em>-Adic Gamma Function and <em>q</em>-Daehee Polynomials and Numbers. Preprints. https://doi.org/10.20944/preprints201802.0118.v1
Chicago/Turabian Style
Duran, U. and Mehmet Acikgoz. 2018 "Some Relationships Including <em>p</em>-Adic Gamma Function and <em>q</em>-Daehee Polynomials and Numbers" Preprints. https://doi.org/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.
Keywords
p-adic numbers; p-adic gamma function; p-adic Euler constant; q-Daehee polynomials; Stirling numbers of the first kind
Subject
Computer Science and Mathematics, Algebra and Number Theory
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.