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

摘要

The aim of this paper is to construct p-adic distribution, on X⊂Cp, of the unification of the Bernoulli, Euler and Genocchi polynomials Yn,β(x;k,a,b), which is given byμn,β,k,a,bj+dpNZp=ab(dpN-p)(dpN)n-kβajbYn,βdpNjdpN,k,adpN,b,where Yn,β(x;k,a,b) are defined by (1.1). We give some applications related to these functions and distribution.