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

Abstract

Abstract The aim of this paper is to construct p-adic distribution, on X ⊂ C p , of the unification of the Bernoulli, Euler and Genocchi polynomials Y n , β ( x ; k , a , b ) , which is given by μ n , β , k , a , b j + dp N Z p = a b ( dp N - p ) ( dp N ) n - k β a jb Y n , β dp N j dp N , k , a dp N , b , where Y n , β ( x ; k , a , b ) are defined by (1.1) . We give some applications related to these functions and distribution.