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Open AccessArticle

Some Identities Involving Two-Variable Partially Degenerate Hermite Polynomials Induced from Differential Equations and Structure of Their Roots

1
Department of Mathematics, Dong-A University, Busan 604-714, Korea
2
Department of Mathematics, Hannam University, Daejeon 34430, Korea
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Author to whom correspondence should be addressed.
Mathematics 2020, 8(4), 632; https://doi.org/10.3390/math8040632
Received: 23 March 2020 / Revised: 16 April 2020 / Accepted: 17 April 2020 / Published: 20 April 2020
(This article belongs to the Special Issue Nonlinear Equations: Theory, Methods, and Applications)
In this paper, we introduce two-variable partially degenerate Hermite polynomials and get some new symmetric identities for two-variable partially degenerate Hermite polynomials. We study differential equations induced from the generating functions of two-variable partially degenerate Hermite polynomials to give identities for two-variable partially degenerate Hermite polynomials. Finally, we study the symmetric properties of the structure of the roots of the two-variable partially degenerate Hermite equations. View Full-Text
Keywords: differential equations; symmetric identities; partially degenerate Hermite polynomials; complex zeros differential equations; symmetric identities; partially degenerate Hermite polynomials; complex zeros
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Hwang, K.-W.; Ryoo, C.S. Some Identities Involving Two-Variable Partially Degenerate Hermite Polynomials Induced from Differential Equations and Structure of Their Roots. Mathematics 2020, 8, 632.

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