Cobalancing hybrid numbers. (English) Zbl 07904196
Summary: 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.
MSC:
| 11B37 | Recurrences |
| 11B39 | Fibonacci and Lucas numbers and polynomials and generalizations |
| 11D04 | Linear Diophantine equations |
References:
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