Cobalancing hybrid numbers

Mariola Rubajczyk, Anetta Szynal-Liana

Abstract


Hybrid numbers are generalization of complex, hyperbolic and dual numbers. In this paper, we define and study hybrid numbers with cobalancing and Lucas-cobalancing coefficients. We derive some fundamental identities for these numbers, among others the Binet formulas and the general bilinear index-reduction formulas which imply the Catalan, Cassini, Vajda, d’Ocagne and Halton identities. Moreover, the generating functions for cobalancing and Lucas-cobalancing hybrid numbers are presented.

Keywords


Cobalancing numbers; Diophantine equation; hybrid numbers; Binet formula

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References


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DOI: http://dx.doi.org/10.17951/a.2024.78.1.87-95
Date of publication: 2024-07-29 22:47:27
Date of submission: 2024-07-11 14:43:33


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