Fibonacci and Lucas Differential Equations

Erkuş-Duman E., Çiftci H.

Application and applied mathematics, vol.13, no.2, pp.756-763, 2018 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 2
  • Publication Date: 2018
  • Journal Name: Application and applied mathematics
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.756-763
  • Keywords: Fibonacci Polynomial, Lucas Polynomial, Recurrence Relation, Gaussian Function, Hypergeometric Differential Equation, GENERALIZED FIBONACCI, POLYNOMIALS
  • Gazi University Affiliated: Yes


The second-order linear hypergeometric differential equation and the hypergeometric function play a central role in many areas of mathematics and physics. The purpose of this paper is to obtain differential equations and the hypergeometric forms of the Fibonacci and the Lucas polynomials. We also write again these polynomials by means of Olver's hypergeometric functions. In addition, we present some relations between these polynomials and the other well-known functions.