On the generalized k-Fibonacci hyperbolic functions

Ipek A.

Ars Combinatoria, vol.97 A, pp.467-484, 2010 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 97 A
  • Publication Date: 2010
  • Journal Name: Ars Combinatoria
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.467-484
  • Keywords: Fibonacci hyperbolic functions, Hyperbolic functions
  • Hatay Mustafa Kemal University Affiliated: Yes

Abstract

The hyperbolic Fibonacci function, which is the being extension of Binet's formula for the Fibonacci number in continuous domain, transform the Fibonacci number theory into "continuous" theory because every identity for the hyperbolic Fibonacci function has its discrete analogy in the framework of the Fibonacci number. In this new paper, it is defined three important generalizations of the kFibonacci sine, cosine and quasi-sine hyperbolic functions and then many number of concepts and techniques that we learned in a standard setting for the k-Fibonacci sine, cosine and quasi-sine hyperbolic functions is carried over to the generalizations of these functions.