The Boole Polynomials Associated with the p-adic Gamma Function
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KünyeDuran, U., Acikgoz, M. (2019). The Boole polynomials associated with the p-adic gamma function. Publications de l'Institut Mathematique, 106(120), 105-112. https://doi.org/10.2298/PIM1920105D
We 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.