Received June 18, 2022. Published online March 3, 2023.
Abstract: In this paper, a new generalization of Mersenne bihyperbolic numbers is introduced. Some of the properties of presented numbers are given. A general bilinear index-reduction formula for the generalized bihyperbolic Mersenne numbers is obtained. This result implies the Catalan, Cassini, Vajda, d'Ocagne and Halton identities. Moreover, generating function and matrix generators for these numbers are presented.
Affiliations: Dorota Bród (corresponding author), Anetta Szynal-Liana, Rzeszow University of Technology, The Faculty of Mathematics and Applied Physics, al. Powstańców Warszawy 12, 35-959 Rzeszów, Rzeszów, Poland, e-mail: email@example.com, firstname.lastname@example.org