- Hacettepe Journal of Mathematics and Statistics
- Vol: 52 Issue: 3
- Special transforms of the generalized bivariate Fibonacci and Lucas polynomials
Special transforms of the generalized bivariate Fibonacci and Lucas polynomials
Authors : Nazmiye Yilmaz, Ibrahim Aktaş
Pages : 640-651
Doi:10.15672/hujms.1110311
View : 193 | Download : 344
Publication Date : 2023-05-30
Article Type : Research Article
Abstract :This paper deals with the Catalan, Hankel, binomial transforms of the generalized bivariate Fibonacci and Lucas polynomials. Also, some useful results such as generating functions, Binet formulas, summations of transforms defined by using recurrence relations of these special polynomials are presented. Furthermore, certain important relations among these transforms are deduced by using obtained new formulas. Finally, the Catalan, Cassini, Vajda and d\'Ocagne formulas for these transforms are also derived.Keywords : binomial transform, bivariate Fibonacci polynomials, Catalan transform, Hankel transform, Horadam polynomials