Fibonacci and Lucas Differential Equations

Erkuş-Duman E., Çiftci H.

Application and applied mathematics, cilt.13, sa.2, ss.756-763, 2018 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 2
  • Basım Tarihi: 2018
  • Dergi Adı: Application and applied mathematics
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.756-763
  • Anahtar Kelimeler: Fibonacci Polynomial, Lucas Polynomial, Recurrence Relation, Gaussian Function, Hypergeometric Differential Equation, GENERALIZED FIBONACCI, POLYNOMIALS
  • Gazi Üniversitesi Adresli: Evet

Özet

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.