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Research Article | Open Access

Novel identities for elementary and complete symmetric polynomials with diverse applications

Ahmed Arafat1,2( ), Moawwad El-Mikkawy2
Department of Mathematics, University of Technology and Applied Sciences, ALRustaq 329, Rustaq, Oman
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
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Abstract

This article aims to present novel identities for elementary and complete symmetric polynomials and explore their applications, particularly to generalized Vandermonde and special tri-diagonal matrices. It also extends existing results on Jacobi polynomials Pn(α,β)(x) and introduces an explicit formula based on the zeros of Pn−1(α,β)(x). Several illustrative examples are included.

Keywords

elementary symmetric polynomialscomplete symmetric polynomialsSchur convexityVandermonde matrixtri-diagonal matrixJacobi polynomials
CLC number: 05E05, 30C15, 33C45, 11C20

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AIMS Mathematics
Volume 9 Issue 9,
September 2024
Pages 23489-23511
DOI: 10.3934/math.20241142

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Cite this article:
Arafat A, El-Mikkawy M. Novel identities for elementary and complete symmetric polynomials with diverse applications. AIMS Mathematics, 2024, 9(9): 23489-23511. https://doi.org/10.3934/math.20241142

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Received: 31 May 2024
Revised: 18 July 2024
Accepted: 25 July 2024
Published: 15 September 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)