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Journals / Gazi University Journal of Science / 2020 / Cilt: 33 - Sayı: 2

On Cauchy Numbers and Their Generalizations

Levent KARGIN
Pages
456–474
Publication Date
2022-10-19
DOI
—
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AI Summary & Key Takeaways

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

Inparticular, these results give rise to new identities for Cauchy numbers.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This paper is concerned with both kinds of the Cauchy numbers and their generalizations.
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Key Findings & Data:Takinginto account Mellin derivative, we relate 𝑝-Cauchy numbers of the second kind with shiftedCauchy numbers of the first kind, which yields new explicit formulas for the Cauchy numbers ofthe both kind.
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Conclusion & Impact:Inparticular, these results give rise to new identities for Cauchy numbers.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

This paper is concerned with both kinds of the Cauchy numbers and their generalizations. Takinginto account Mellin derivative, we relate 𝑝-Cauchy numbers of the second kind with shiftedCauchy numbers of the first kind, which yields new explicit formulas for the Cauchy numbers ofthe both kind. We introduce a generalization of the Cauchy numbers and investigate severalproperties, including recurrence relations, convolution identities and generating functions. Inparticular, these results give rise to new identities for Cauchy numbers.

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Cite This Article

KARGIN, L. (2022). On Cauchy Numbers and Their Generalizations. Gazi University Journal of Science, Cilt: 33 - Sayı: 2, 456–474. https://ajindex.com/articles/521286

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