A Study on Dual Hyperbolic Generalized Pandita Numbers

This paper introduces the framework of generalized dual hyperbolic Pandita numbers, contributing a novel class of structured sequences to the expanding domain of number theory. Anchored in the principles of dual and hyperbolic systems, these constructs pave the way for exploring algebraic symmetries and recursive behaviors beyond classical formulations. Particular attention is devoted to notable special cases, including the dual hyperbolic Pandita and dual hyperbolic Pandita-Lucas numbers, whose properties are meticulously examined. To deepen understanding and facilitate computation, we derive explicit closed-form representations using Binet-type formulations, construct generating mechanisms through formal power series, and establish summative expressions with broad applicability. Additionally, matrix-based representations are developed to offer an algebraic lens through which structural dynamics can be modeled and analyzed. These formulations not only enrich the theoretical foundations of discrete mathematics and symbolic computation but also highlight promising applications in engineering disciplines—particularly in the modeling of iterative systems, signal transformations, and the analysis of complex networks. The insights presented herein lay groundwork for future exploration into hybrid sequence systems and their role in interdisciplinary problem solving.