On Mahler Expansion of p-adic gamma Function Affiliated With the q-boole Polynomials
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CitationDuran, U., Acikgoz, M. (2019). On Mahler Expansion of p-adic gamma Function Affiliated With the q-boole Polynomials. Advances and Applications In Mathematical Sciences, 18 (7), pp. 533-544.
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.