Hyperbolic functions with second order recurrence sequences

Kocer E. G. , TUĞLU N., Stakhov A.

ARS COMBINATORIA, vol.88, pp.65-81, 2008 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 88
  • Publication Date: 2008
  • Journal Name: ARS COMBINATORIA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.65-81
  • Keywords: Fibonacci numbers, Pell numbers, hyperbolic functions, FIBONACCI, NUMBERS
  • Gazi University Affiliated: Yes


In this paper, we introduce an extension of the hyperbolic Fibonacci and Lucas functions which were studied by Stakhov and Rozin. Namely, we define hyperbolic functions by second order recurrence sequences and study their hyperbolic and recurrence properties. We give the corollaries for Fibonacci, Lucas, Pell and Pell-Lucas numbers. We finalize with the introduction some surfaces (the Metallic Shofars) that relate to the hyperbolic functions with the second order recurrence sequences.