Special transforms of the generalized bivariate Fibonacci and Lucas polynomials

Authors : Nazmiye YILMAZ, İbrahim AKTAŞ

Pages : 640-651

Doi:10.15672/hujms.1110311

View : 203 | Download : 345

Publication Date : 2023-05-30

Article Type : Research Paper

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