One-parameter generalization of dual-hyperbolic Jacobsthal numbers - Bród, Dorota; Szynal-Liana, Anetta; Włoch, Iwona (Annales Mathematicae Silesianae, 2023)
In this paper, we introduce one-parameter generalization of dualhyperbolic Jacobsthal numbers – dual-hyperbolic r-Jacobsthal numbers. We present some properties of them, among others the Binet formula, Catalan, Cassini, and d’Ocagne identities. Moreover, we give the generating function and summation formula for these numbers. The presented results are a generalization of the results for the dual-hyperbolic Jacobsthal numbers.