Novel Classes on Generating Functions of the Products of (p,q)-Modified Pell Numbers with Several Bivariate Polynomials

Ali Boussayoud, Salah Boulaaras () and Ali Allahem
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Ali Boussayoud: LMAM Laboratory, Department of Mathematics, Faculty of Exact Sciences and Informatics, Mohamed Seddik Ben Yahia University, Jijel 18000, Algeria
Salah Boulaaras: Department of Mathematics, College of Sciences, Qassim University, Buraydah 51452, Saudi Arabia
Ali Allahem: Department of Mathematics, College of Sciences, Qassim University, Buraydah 51452, Saudi Arabia

Mathematics, 2024, vol. 12, issue 18, 1-24

Abstract: In this paper, using the symmetrizing operator δ e 1 e 2 2 − l , we derive new generating functions of the products of p , q -modified Pell numbers with various bivariate polynomials, including Mersenne and Mersenne Lucas polynomials, Fibonacci and Lucas polynomials, bivariate Pell and bivariate Pell Lucas polynomials, bivariate Jacobsthal and bivariate Jacobsthal Lucas polynomials, bivariate Vieta–Fibonacci and bivariate Vieta–Lucas polynomials, and bivariate complex Fibonacci and bivariate complex Lucas polynomials.

Keywords: symmetric functions; generating functions; bivariate Jacobsthal polynomials; ( p , q )-modified Pell numbers; bivariate Vieta–Fibonacci polynomials; bivariate Mersenne Lucas polynomials; nonlinear equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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