Symmetric and generating functions of generalized (p,q)-numbers
Nabiha Saba, Ali Boussayoud, Abdelhamid Abderrezzak
Abstract
In this paper, we will firstly define a new generalization of numbers (p, q) and then derive the appropriate Binet's formula and generating functions concerning (p,q)-Fibonacci numbers, (p,q)- Lucas numbers, (p,q)-Pell numbers, (p,q)-Pell Lucas numbers, (p,q)-Jacobsthal numbers and (p,q)-Jacobsthal Lucas numbers. Also, some useful generating functions are provided for the products of (p,q)-numbers with bivariate complex Fibonacci and Lucas polynomials.
Topics & Concepts
Lucas numberFibonacci polynomialsFibonacci numberMathematicsLucas sequencePisano periodCombinatoricsRecurrence relationDiscrete mathematicsGenerating functionGeneralizationClassical orthogonal polynomialsOrthogonal polynomialsMathematical analysisAdvanced Mathematical Theories and ApplicationsAdvanced Mathematical IdentitiesAdvanced Combinatorial Mathematics