Generating Functions For Two-Variable Polynomials Related To a Family of Fibonacci Type Polynomials and Numbers

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OZDEMIR G., ŞİMŞEK Y.

FILOMAT, vol.30, no.4, pp.969-975, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 4
  • Publication Date: 2016
  • Doi Number: 10.2298/fil1604969o
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.969-975
  • Keywords: Fibonacci numbers, Fibonacci polynomials, Jacobsthal polynomials, Chebyshev polynomials, Vieta-Fibonacci polynomials, Vieta-Lucas polynomials, Humbert polynomials, Geganbauer polynomials, generating functions
  • Akdeniz University Affiliated: Yes

Abstract

The purpose of this paper is to construct generating functions for the family of the Fibonacci and Jacobsthal polynomials. Using these generating functions and their functional equations, we investigate some properties of these polynomials. We also give relationships between the Fibonacci, Jacobsthal, Chebyshev polynomials and the other well known polynomials. Finally, we give some infinite series applications related to these polynomials and their generating functions.