Received March 22, 2025. Published online October 2, 2025.
Abstract: We describe new classes of dual and hyper-dual numbers whose coefficients consist of the $k$-Leonardo numbers. We will call these numbers dual $k$-Leonardo numbers and hyper-dual $k$-Leonardo numbers, respectively. Then we examine several fundamental properties associated with the dual and hyper-dual $k$-Leonardo numbers, including recurrence relations, Binet-like formula, ordinary generating function, exponential generating function, and some identities such as Catalan and d'Ocagne.
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Affiliations: Tülay Yağmur, Department of Mathematics, Aksaray University, 68100, Aksaray, Turkey, e-mail: tulayyagmurr@gmail.com
