The forms of $ (q, h) $-difference equation and the roots structure of their solutions with degenerate quantum Genocchi polynomials

Jung Yoog Kang; Cheon Seoung Ryoo; Jung Yoog Kang; Cheon Seoung Ryoo

doi:10.3934/math.20241436

AIMS Mathematics

2024, Volume 9, Issue 11: 29645-29661. doi: 10.3934/math.20241436

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The forms of $ (q, h) $-difference equation and the roots structure of their solutions with degenerate quantum Genocchi polynomials

Jung Yoog Kang ¹,
Cheon Seoung Ryoo ^{2
,
,}

1.
Department of Mathematics Education, Silla University, Busan, 46958, Republic of Korea
2.
Department of Mathematics, Hannam University, Daejeon, 34430, Republic of Korea

Received: 31 August 2024 Revised: 14 October 2024 Accepted: 15 October 2024 Published: 18 October 2024
MSC : 33C45, 35B06, 39A05, 65H04

We construct a new type of Genocchi polynomials using degenerate quantum exponential functions and find various forms of $ (q, h) $-difference equations with these polynomials as solutions. This paper includes properties of the symmetric structures of $ (q, h) $-difference equations and also presents $ (q, h) $-difference equations with other polynomials as coefficients. By understanding the approximate roots structure of degenerate quantum Genocchi polynomials (DQG), which are common solutions to various forms of $ (q, h) $-difference equations, we identify the properties of the solutions.
- $ (q, h) $-derivative,
- degenerate quantum Genocchi (DQG) polynomials,
- approximate root,
- $ (q, h) $-difference equation
Citation: Jung Yoog Kang, Cheon Seoung Ryoo. The forms of $ (q, h) $-difference equation and the roots structure of their solutions with degenerate quantum Genocchi polynomials[J]. AIMS Mathematics, 2024, 9(11): 29645-29661. doi: 10.3934/math.20241436

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Abstract

We construct a new type of Genocchi polynomials using degenerate quantum exponential functions and find various forms of $ (q, h) $-difference equations with these polynomials as solutions. This paper includes properties of the symmetric structures of $ (q, h) $-difference equations and also presents $ (q, h) $-difference equations with other polynomials as coefficients. By understanding the approximate roots structure of degenerate quantum Genocchi polynomials (DQG), which are common solutions to various forms of $ (q, h) $-difference equations, we identify the properties of the solutions.

References

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