Symmetric and generating functions of generalized (p,q)-numbers | Zendy

Nabiha Saba | Zendy; Ali Boussayoud | Zendy; Abdelhamid Abderrezzak | Zendy

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Symmetric and generating functions of generalized (p,q)-numbers

Author(s) -

Nabiha Saba,

Ali Boussayoud,

Abdelhamid Abderrezzak

Publication year - 2021

Publication title -

kuwait journal of science

Language(s) - English

Resource type - Journals

eISSN - 2307-4116

pISSN - 2307-4108

DOI - 10.48129/kjs.v48i4.10074

Subject(s) - lucas number , fibonacci polynomials , fibonacci number , mathematics , lucas sequence , pisano period , combinatorics , recurrence relation , discrete mathematics , generating function , generalization , classical orthogonal polynomials , orthogonal polynomials , mathematical analysis

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.

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