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Keywords:
dual numbers; hyper-dual numbers; Leonardo numbers; $k$-Leonardo numbers
dual numbers; hyper-dual numbers; Leonardo numbers; $k$-Leonardo numbers
Summary:
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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