On the p-Adic Integral Representation of Bernstein Polynomials Associated with (h, q)-Genocchi Numbers and Polynomials

Throughout this paper, let p be a fixed odd prime number. The symbol, Zp, Qp and Cp denote the ring of p-adic integers, the field of p-adic rational numbers and the completion of algebraic closure of Qp. Let N be the set of natural numbers and Z+ = N ∪ {0}. As well known definition, the p-adic absolute value is given by |x|p = p−r where x = p t s with (t, p) = (s, p) = (t, s) = 1. When one talks of q-extension, q is variously considered as an indeterminate, a complex number q ∈ C, or a p-adic number q ∈ Cp. In this paper we assume that q ∈ Cp with |1 − q|p < 1. We assume that UD(Zp) is the space of the uniformly differentiable function on Zp. For f ∈ UD(Zp), Kim defined the fermionic p-adic invariant integral on Zp