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

Asian-European Journal of Mathematics, pp.22501194, 2021 (Journal Indexed in ESCI)

• Publication Type: Article / Article
• Publication Date: 2021
• Doi Number: 10.1142/s1793557122501194
• Title of Journal : Asian-European Journal of Mathematics
• Page Numbers: pp.22501194

#### 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 $C{J}_{k,n}^{l}$by using Hankel transform. Then we define the incomplete $h\left(x\right)$-Jacobsthal polynomials. Then we examine the recurrence relation and some properties of these polynomials.