Preprint Article Version 1 This version is not peer-reviewed

The Boole Polynomials Associated with the p-adic Gamma Function

Version 1 : Received: 15 May 2019 / Approved: 16 May 2019 / Online: 16 May 2019 (15:34:31 CEST)

How to cite: Duran, U.; Acikgoz, M. The Boole Polynomials Associated with the p-adic Gamma Function. Preprints 2019, 2019050216 (doi: 10.20944/preprints201905.0216.v1). Duran, U.; Acikgoz, M. The Boole Polynomials Associated with the p-adic Gamma Function. Preprints 2019, 2019050216 (doi: 10.20944/preprints201905.0216.v1).

Abstract

The main aim of this paper is to set some correlations between Boole polynomials and p-adic gamma function in conjunction with p-adic Euler contant. We develop diverse formulas for p-adic gamma function by means of their Mahler expansion and fermionic p-adic integral on ℤ_{p}. Also, we acquire two fermionic p-adic integrals of p-adic gamma function in terms of Boole numbers and polynomials. We then provide fermionic p-adic integral of the derivative of p-adic gamma function and a representation for the p-adic Euler constant by means of the Boole polynomials. Furthermore, we investigate an explicit representation for the aforesaid constant covering Stirling numbers of the first kind.

Subject Areas

p-adic numbers, p-adic gamma function, p-adic Euler constant, Mahler expansion, Boole polynomials, Stirling numbers of the first kind.

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