The q-pell Hyperbolic Functions

Guncan A., Akduman S.

International Conference of Numerical Analysis and Applied Mathematics (ICNAAM), Kos, Greece, 19 - 25 September 2012, vol.1479, pp.942-945 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 1479
  • Doi Number: 10.1063/1.4756298
  • City: Kos
  • Country: Greece
  • Page Numbers: pp.942-945


In 2005 Stakhov and Rozin introduced a new class of hyperbolic functions which is called Fibonacci hyperbolic functions. The aim of this study to give q-analogue of the Pell hyperbolic functions. These functions can be regarded as q extensions of classical hyperbolic functions. We introduce the q-analogue of classical Silver ratio as follow delta(q) = 1+q(n-1)/2 + root 4q(n-2)+(1+q(n-1))(2)/2 , n >= 2. Making use of this q-analogue of the Silver ratio, we defined sin P(q)h(x) and cos P(q)h(x) functions. We investigated some properties and gave some relationships between these functions.