P-Adic distribution of the unification of the Bernoulli, Euler and Genocchi polynomials

Abstract

The aim of this paper is to construct p-adic distribution, on X subset of C-p, of the unification of the Bernoulli, Euler and Genocchi polynomials Y-n,Y-beta(x; k, a, b), which is given by

mu(n,beta,k,a,b) (j + dp(N)Z(p)) = a(b(dpN-p)) (dp(N))(n-k)(beta/a)(jb) Y-n,Y-beta dpN (j/dp(N), k, a(dpN), b),

where Y-n,Y-beta (x; k, a, b) are defined by (1.1). We give some applications related to these functions and distribution