On Generalized Fibonacci Polynomials: Horadam Polynomials
Yüksel Soykan
Abstract
In this paper, we investigate the generalized Fibonacci (Horadam) polynomials and we deal with, in detail, two special cases which we call them $(r,s)$-Fibonacci and $(r,s)$-Lucas polynomials. We present Binet's formulas, generating functions, Simson's formulas, and the summation formulas for these polynomial sequences. Moreover, we give some identities and matrices associated with these sequences. Finally, we present several expressions and combinatorial results of the generalized Fibonacci polynomials.
Topics & Concepts
Fibonacci polynomialsFibonacci numberMathematicsLucas numberPisano periodClassical orthogonal polynomialsWilson polynomialsDifference polynomialsOrthogonal polynomialsCombinatoricsRecurrence relationDiscrete orthogonal polynomialsPolynomialLucas sequenceDiscrete mathematicsPure mathematicsAlgebra over a fieldMathematical analysisAdvanced Mathematical Theories and ApplicationsFractal and DNA sequence analysisAdvanced Mathematical Identities