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

Author

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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)

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.

Suggested Citation

  • Cheon-Seoung Ryoo & Jungyoog Kang, 2021. "Some Properties Involving q -Hermite Polynomials Arising from Differential Equations and Location of Their Zeros," Mathematics, MDPI, vol. 9(11), pages 1-12, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1168-:d:559948
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    Cited by:

    1. Arsen Palestini, 2022. "Preface to the Special Issue “Mathematical Modeling with Differential Equations in Physics, Chemistry, Biology, and Economics”," Mathematics, MDPI, vol. 10(10), pages 1-2, May.

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