The q-Fibonacci Hyperbolic Functions


Guncan A., Erbil Y.

International Conference of Numerical Analysis and Applied Mathematics (ICNAAM), Kos, Greece, 19 - 25 September 2012, vol.1479, pp.946-949 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 1479
  • Doi Number: 10.1063/1.4756299
  • City: Kos
  • Country: Greece
  • Page Numbers: pp.946-949

Abstract

In 2005 Stakhov and Rozin introduced a new class of hyperbolic functions which is called Fibonacci hyperbolic functions. In this paper, we study q-analogue of Fibonacci hyperbolic functions. These functions can be regarded as q extensions of classical hyperbolic functions. We introduce the q-analogue of classical Golden ratio as follow phi(q) = 1+root 1+4q(n-2)/2 n >= 2. Making use of this q-analogue of the Golden ratio, we defined sinF(q)h(x) and cosF(q)h(x) functions. We investigated some properties and gave some relationships between these functions.