Some New Identities with Respect to Bihyperbolic Fibonacci and Lucas Numbers

  • Ayşe Zeynep Azak Sakarya University Faculty of Education Mathematics and Science Education Department 54300 Hendek, Sakarya, Turkey
Keywords: Bihyperbolic numbers, generalized bihyperbolic Fibonacci numbers, bihyperbolic Lucas numbers, hyperbolic four-complex numbers


In this paper, we define bihyperbolic Lucas numbers, bihyperbolic generalized Fibonacci numbers and give some algebraic properties of these numbers. Then, some identities concerning conjugations, Honsberger's identity, negabihyperbolic numbers for bihyperbolic Fibonacci number and bihyperbolic Lucas numbers have been derived. Finally, well-known identities have been represented such as Cassini's, Catalan's, d'Ocagne's identities and Binet formula for bihyperbolic Lucas and bihyperbolic generalized Fibonacci numbers. Also, special cases of these identities and formulas have been given.


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