Generating Functions of Binary Products of Gaussian Numbers and Special Bivariate Polynomials at conecutive and nonconecutive terms.

Ali Boussayoud; Dounya  Hamek; Dalal  Alhwikem; Dalal  Alhwikem; Nesrine Harrouche

doi:10.5269/bspm.81523

Generating Functions of Binary Products of Gaussian Numbers and Special Bivariate Polynomials at conecutive and nonconecutive terms.

Ali Boussayoud LMAM Laboratory and Department of Mathematics, Mohamed Seddik Ben Yahia University, Jijel,
Dounya Hamek LMEPA Laboratory Materials Mohamed Seddik Ben Yahia University, Jijel, Algeria
Dalal Alhwikem Department of Mathematics, College of Science, Qassim University, Buraydah 52571, Saudi Arabia
Dalal Alhwikem Department of Mathematics, College of Science, Qassim University, Buraydah 52571, Saudi Arabia
Nesrine Harrouche Faculty of Exact Sciences and Computer Science Department of mathematics, Mohamed Seddik Ben Yahia University, Jijel, Algeria

Abstract

In this research, we prove a new theorem by applying the symmetrizing operator k+l s+1a1a2 . This theorem allows us to introduce a novel family of generating functions for the products of Gaussian Pell-Padovan and Gaussian Perrin with some (p;q)-numbers, as well as special bivariate polynomials with consecutive and nonconsecutive indices.