Some Properties Involving q -Hermite Polynomials Arising from Differential Equations and Location of Their Zeros

Cheon-Seoung Ryoo and Jungyoog Kang
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Cheon-Seoung Ryoo: Department of Mathematics, Hannam University, Daejeon 34430, Korea
Jungyoog Kang: Department of Mathematics Education, Silla University, Busan 46958, Korea

Mathematics, 2021, vol. 9, issue 11, 1-12

Abstract: Hermite polynomials are one of the Apell polynomials and various results were found by the researchers. Using Hermit polynomials combined with q -numbers, we derive different types of differential equations and study these equations. From these equations, we investigate some identities and properties of q -Hermite polynomials. We also find the position of the roots of these polynomials under certain conditions and their stacked structures. Furthermore, we locate the roots of various forms of q -Hermite polynomials according to the conditions of q -numbers, and look for values which have approximate roots that are real numbers.

Keywords: q -Hermite polynomials; zeros of q -Hermite polynomials; differential equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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