Exploring Zeros of Hermite- λ Matrix Polynomials: A Numerical Approach

Maryam Salem Alatawi, Manoj Kumar, Nusrat Raza () and Waseem Ahmad Khan
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Maryam Salem Alatawi: Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia
Manoj Kumar: Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
Nusrat Raza: Mathematics Section, Women’s College, Aligarh Muslim University, Aligarh 202002, India
Waseem Ahmad Khan: Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia

Mathematics, 2024, vol. 12, issue 10, 1-17

Abstract: This article aims to introduce a set of hybrid matrix polynomials associated with λ -polynomials and explore their properties using a symbolic approach. The main outcomes of this study include the derivation of generating functions, series definitions, and differential equations for the newly introduced two-variable Hermite λ -matrix polynomials. Furthermore, we establish the quasi-monomiality property of these polynomials, derive summation formulae and integral representations, and examine the graphical representation and symmetric structure of their approximate zeros using computer-aided programs. Finally, this article concludes by introducing the idea of 1-variable Hermite λ matrix polynomials and their structure of zeros using a computer-aided program.

Keywords: trigonometric functions; symbolic operator; hermite polynomials; ?-polynomials; distribution of zeros (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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