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Journals / Konuralp Journal of Mathematics / 2026 / Volume: 14 Issue: 1

Some Properties of the Peter-Genocchi Polynomials with Location of Their Zeros

Uğur Duran(İSKENDERUN TEKNİK ÜNİVERSİTESİ)0000-0002-5717-1199
Mehmet Açıkgöz(Gaziantep Üniversitesi)0000-0003-1091-9697
Waseem Ahmad Khan(Prince Mohammad Bin Fahd University)0000-0002-4681-9885
Cheon Seoung Ryoo(Hannam University)0000-0002-4647-1380
Pages
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Publication Date
2026-04-30
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we provide several graphical representations and a list in a table for certain zero values of the Peter-Genocchi polynomials, enhancing the understanding of the numerical data and facilitating a more intuitive grasp of the concepts discussed.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Recently, the Changhee-Genocchi polynomials and the Boole-Genocchi polynomials have been considered with their various extensions and many of their applications, and properties have been investigated.
📊
Key Findings & Data:Inspired by these developments, in this paper, we introduce the Peter-Genocchi polynomials (or say higher-order Boole-Genocchi polynomials) and then explore some of their fundamental properties and formulas, including some summation formulas, addition formulas, symmetric identities, and an implicit summation formula.
💡
Conclusion & Impact:Finally, we provide several graphical representations and a list in a table for certain zero values of the Peter-Genocchi polynomials, enhancing the understanding of the numerical data and facilitating a more intuitive grasp of the concepts discussed.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Genocchi polynomials · Peter polynomials · Changhee polynomials

Abstract

Recently, the Changhee-Genocchi polynomials and the Boole-Genocchi polynomials have been considered with their various extensions and many of their applications, and properties have been investigated. Inspired by these developments, in this paper, we introduce the Peter-Genocchi polynomials (or say higher-order Boole-Genocchi polynomials) and then explore some of their fundamental properties and formulas, including some summation formulas, addition formulas, symmetric identities, and an implicit summation formula. Also, for the Peter-Genocchi polynomials, we provide diverse correlations associated with the higher-order Genocchi polynomials, Stirling numbers of both kinds, and higher-order Daehee polynomials. Moreover, we investigate some derivative properties and a differential operator formula for the Peter-Genocchi polynomials. Finally, we provide several graphical representations and a list in a table for certain zero values of the Peter-Genocchi polynomials, enhancing the understanding of the numerical data and facilitating a more intuitive grasp of the concepts discussed.

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Cite This Article

Duran, U., Açıkgöz, M., Khan, W. A., Ryoo, C. S. (2026). Some Properties of the Peter-Genocchi Polynomials with Location of Their Zeros. Konuralp Journal of Mathematics, Volume: 14 Issue: 1. https://ajindex.com/articles/1521437

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