The Boole Polynomials Associated with the p-adic Gamma Function
Keyword(s):
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.
Keyword(s):
2019 ◽
Vol 15
(01)
◽
pp. 67-84
◽
2021 ◽
Vol 27
(2)
◽
pp. 101-110