Affiliation:
1. 1 Rzeszow University of Technology , The Faculty of Mathematics and Applied Physics , al. Powstańców Warszawy 12 35-959 Rzeszów Poland
Abstract
Abstract
In this paper, we introduce one-parameter generalization of dual-hyperbolic 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.