On Tricomplex Ernst-type sequence
Keywords:
Binet formula, Ernst sequence, Tricomplex Ernst sequence, Tagiuri-Vajda's identityAbstract
In this article, we present two new sequences of Ernst-type that mark a significant step in the theoretical exploration of such mathematical constructions. Specifically, we develop the concept of Ernst and Ernst-Lucas tricomplex numbers, offering a detailed analysis of their properties and their links to classical Ernst numbers. We establish several fundamental identities that clarify the properties and structure of these sequences. In addition, we derive the generating function for this new class of sequences and propose a Binet-type formula. Our research also validates several classical identities related to Ernst tricomplex numbers, including those attributed to Tagiuri-Vajda, d'Ocagne, Catalan and Cassini. This research not only improves our understanding of these distinctive sequences, but also provides a solid foundation for future research in this emerging domain.Downloads
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