Special transforms of the generalized bivariate Fibonacci and Lucas polynomials
Nazmiye Yılmaz, İbrahim Aktaş
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.
Topics & Concepts
MathematicsFibonacci numberFibonacci polynomialsBivariate analysisCatalan numberLucas numberBinomial coefficientBinomial (polynomial)Recurrence relationClassical orthogonal polynomialsOrthogonal polynomialsCatalanWilson polynomialsPure mathematicsDiscrete orthogonal polynomialsDifference polynomialsAlgebra over a fieldCombinatoricsStatisticsHumanitiesPhilosophyAdvanced Mathematical Theories and ApplicationsAdvanced Mathematical IdentitiesFractal and DNA sequence analysis