Gaussian Numbers with Generalized Pandita Numbers Components

Abstract

In this study, we introduce and investigate a new class of numerical sequences in the complex domain—Gaussian generalized Pandita numbers—which extend the classical theory of linear recurrence relations. In particular, we focus on two distinct cases: the Gaussian Pandita numbers and the Gaussian Pandita-Lucas numbers. For these sequences, we derive and present a comprehensive set of mathematical results, including recurrence relations, closed-form expressions via Binet-type formulas, ordinary and exponential generating functions. In addition, we establish various algebraic identities, provide matrix representations, and prove generalized forms of Simpson’s formula. Summation identities are also developed to further explore the structural and analytical properties of these numbers. The findings contribute to the broader theory of Gaussian integer sequences and open new directions for applications in discrete mathematics and computational number theory.