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

On Cauchy Numbers and Their Generalizations

Levent KARGIN
Sayfa
456–474
Yayın Tarihi
2020-06-01
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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

📌 3 Maddede Bu Makale

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Amaç & Hipotez:This paper is concerned with both kinds of the Cauchy numbers and their generalizations.
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Temel Bulgular & Veri:Taking into account Mellin derivative, we relate p-Cauchy numbers of the second kind with shifted Cauchy numbers of the first kind, which yields new explicit formulas for the Cauchy numbers of the both kind.
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Sonuç & Katkı:In particular, these results give rise to new identities for Cauchy numbers.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Cauchy numbers · Poly-Cauchy numbers · p-Cauchy numbers

Abstract

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

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Bu Makaleye Atıf Yap

KARGIN, L. (2020). On Cauchy Numbers and Their Generalizations. Gazi University Journal of Science, Cilt: 33 - Sayı: 2, 456–474. https://ajindex.com/articles/254728

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Kaynakça (20)

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