# On Hyperbolic Numbers With Generalized Fibonacci Numbers Components

## DOI:

https://doi.org/10.26713/cma.v12i4.1396## Keywords:

Fibonacci numbers, Lucas numbers, Hyperbolic numbers, Hyperbolic Fibonacci numbers, Cassini identity## Abstract

In this paper, we introduce the generalized hyperbolic Fibonacci numbers over the bidimensional Clifford algebra of hyperbolic numbers. As special cases, we deal with hyperbolic Fibonacci and hyperbolic Lucas numbers. We present Binet’s formulas, generating functions and the summation formulas for these numbers. Moreover, we give Catalan’s, Cassini’s, d’Ocagne’s, Gelin-Cesàro’s, Melham’s identities and present matrices related with these sequences.

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## How to Cite

*Communications in Mathematics and Applications*,

*12*(4), 987–1004. https://doi.org/10.26713/cma.v12i4.1396

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