A Study on Dual Hyperbolic Generalised Leonardo Numbers

In this study, we present a comprehensive formalization of dual hyperbolic generalized Leonardo numbers, systematically examining their structural properties and mathematical significance. The dual hyperbolic number system plays a crucial role in mathematical analysis, as its application to numerical sequences leads to the emergence of novel algebraic structures with distinct characteristics and computational advantages. Our analysis focuses on three specific variants of these sequences: Dual hyperbolic modified Leonardo numbers, dual hyperbolic Leonardo-Lucas numbers, and dual hyperbolic Leonardo numbers, each possessing uniquealgebraic and combinatorial features.Furthermore, we rigorously establish a wide array of mathematical identities and matrix representations associated with these sequences, as well as recurrence relations, Binet’s formulae, generating functions, Simpson’s formula, Honsberger’s identity, and several summation formulas that provide deeper insights into the combinatorial and analytical properties of these sequences.