On Mahler Expansion of p-adic Gamma Function Affiliated with the q-Boole Polynomials

Ugur Duran; Mehmet Acikgoz

doi:10.20944/preprints201905.0217.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 15 May 2019 / Approved: 16 May 2019 / Online: 16 May 2019 (15:35:19 CEST)

In this paper, we investigate several relations for p-adic gamma function by means of their Mahler expansion and fermionic p-adic q-integral on ℤ_{p}. We also derive two fermionic p-adic q-integrals of p-adic gamma function in terms of q-Boole polynomials and numbers. Moreover, we discover fermionic p-adic q-integral of the derivative of p-adic gamma function. We acquire a representation for the p-adic Euler constant by means of the q-Boole polynomials. We finally develop a novel, explicit and interesting representation for the p-adic Euler constant including Stirling numbers of the first kind.

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

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On Mahler Expansion of p-adic Gamma Function Affiliated with the q-Boole Polynomials

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