Some new properties of generalized \((p,q)\)-numbers and generating functions for certain products

Volume 34, Issue 4, pp 326--349 https://dx.doi.org/10.22436/jmcs.034.04.02

Publication Date: April 03, 2024 Submission Date: June 22, 2023 Revision Date: November 16, 2023 Accteptance Date: February 19, 2024

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Authors

N. Saba - LMAM Laboratory and Department of Mathematics, Mohamed Seddik Ben Yahia University, Jijel, Algeria. A. Boussayoud - LMAM Laboratory and Department of Mathematics, Mohamed Seddik Ben Yahia University, Jijel, Algeria. K. V. V. Kanuri - 3669 Leatherwood Dr, Frisco, TX 75033, USA.

Abstract

In this paper, we first give some new results and properties on the generalized \(( p,q) \)-numbers including explicit formula, negative extension, etc. After that, by using the complete homogeneous symmetric functions we obtain the new generating functions for the products of some bivariate polynomials with certain \(( p,q) \)-numbers at positive and negative indices.

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Keywords

• Generalized \((p,q) \)-numbers
• bivariate Mersenne polynomials
• bivariate Mersenne Lucas polynomials
• complete homogeneous symmetric functions
• generating functions
• explicit formula

MSC

•  05E05
•  11B39

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