Open AccessSymmetric and generating functions of generalized (p,q)-numbers
Author(s) -
Nabiha Saba,
Ali Boussayoud,
Abdelhamid Abderrezzak
Publication year - 2021
Publication title -
maǧallaẗ al-kuwayt li-l-ʿulūm
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 , lucas sequence , mathematics , pisano period , combinatorics , recurrence relation , generalization , generating function , discrete mathematics , real number , arithmetic , 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.