A Study On Dual Hyperbolic Generalized Edouard Numbers

Abstract

In this research, we introduce the generalized dual hyperbolic Edouard numbers, a novel class of number sequences that extends existing recurrence relations into a new mathematical framework. Several special cases of these numbers are examined in detail, including the dual hyperbolic Edouard numbers and the dual hyperbolic Edouard-Lucas numbers, each revealing intriguing combinatorial and algebraic properties. Explicit expressions for these sequences are derived, such as Binet-type formulas, generating functions, and summation identities, which offer analytical insight into their behavior and structural patterns. In addition, we explore matrix representations associated with these sequences, providing an elegant algebraic tool for further theoretical development and potential applications.