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.
Erkus-Duman, Esra and Ciftci, Hakan
Fibonacci and Lucas Differential Equations,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 13,
2, Article 10.
Available at: https://digitalcommons.pvamu.edu/aam/vol13/iss2/10