A Study On Gaussian Generalized Edouard Numbers

Abstract

This paper examines the properties and applications of Gaussian Generalized Edouard numbers, aiming to enrich the theoretical framework of number sequences. Utilizing analytical and algebraic techniques, we derive novel recurrence relations, sum formulas, and various representations for these sequences. In particular, we establish Binet’s formula, explore generating functions and matrix representations, and present Simson’s formula as an alternative approach. Moreover, we analyze two special cases namely, Gaussian Edouard numbers and Gaussian Edouard-Lucas numbers to emphasize their unique structural characteristics. Our results reveal that these sequences possess distinct combinatorial properties that render them applicable in such as, coding theory. Given the broad applicability of number sequences, it is crucial to differentiate this sequence from others based on its unique attributes. Future research will focus on further investigating its structural uniqueness and exploring additional practical implementations.