Some properties for 2-variable modified partially degenerate Hermite (MPDH) polynomials derived from differential equations and their zeros distributions

Gyung Won Hwang; Cheon Seoung Ryoo; Jung Yoog Kang; Gyung Won Hwang; Cheon Seoung Ryoo; Jung Yoog Kang

doi:10.3934/math.20231564

AIMS Mathematics

2023, Volume 8, Issue 12: 30591-30609. doi: 10.3934/math.20231564

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Some properties for 2-variable modified partially degenerate Hermite (MPDH) polynomials derived from differential equations and their zeros distributions

1.
Department of Mathematics, Dong-A University, Busan 604-714, Republic of Korea
2.
Department of Mathematics, Hannam University, Daejeon 34430, Republic of Korea
3.
Department of Mathematics Education, Silla University, Busan 46958, Republic of Korea

Received: 07 August 2023 Revised: 14 September 2023 Accepted: 26 October 2023 Published: 10 November 2023
MSC : 11B68, 11B83, 26C10, 34A30, 65D20, 65L99

The 2-variable modified partially degenerate Hermite (MPDH) polynomials are the subject of our study in this paper. We found basic properties of these polynomials and obtained several types of differential equations related to MPDH polynomials. Based on the MPDH polynomials, we looked at the structures of the approximation roots for a particular polynomial and checked the values of the approximate roots. Further, we presented some conjectures for MPDH polynomials.
- differential equations,
- symmetric identities,
- partially degenerate Hermite polynomials,
- complex zeros
Citation: Gyung Won Hwang, Cheon Seoung Ryoo, Jung Yoog Kang. Some properties for 2-variable modified partially degenerate Hermite (MPDH) polynomials derived from differential equations and their zeros distributions[J]. AIMS Mathematics, 2023, 8(12): 30591-30609. doi: 10.3934/math.20231564

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Abstract

The 2-variable modified partially degenerate Hermite (MPDH) polynomials are the subject of our study in this paper. We found basic properties of these polynomials and obtained several types of differential equations related to MPDH polynomials. Based on the MPDH polynomials, we looked at the structures of the approximation roots for a particular polynomial and checked the values of the approximate roots. Further, we presented some conjectures for MPDH polynomials.

References

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