On Mahler Expansion of p-adic gamma Function Affiliated With the q-boole Polynomials

Abstract

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.