Catalan transform of the incomplete Jacobsthal numbers and incomplete generalized Jacobsthal polynomials

Abstract

We introduce the Catalan transform of the Incomplete Jacobsthal numbers. We apply the Hankel transform to the Catalan transforms of these numbers. We calculate determinants of matrixes formed with [Formula: see text]by using Hankel transform. Then we define the incomplete h(x)-Jacobsthal polynomials. Then we examine the recurrence relation and some properties of these polynomials.