On generalized bihyperbolic Mersenne numbers

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.

Keywords

• mersenne number
• hyperbolic number
• bihyperbolic number
• recurrence relation