On Cauchy Numbers and Their Generalizations

Year 2020, Volume: 33 Issue: 2, 456 - 474, 01.06.2020

Levent Kargın

https://doi.org/10.35378/gujs.604550

Cited By: 4

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. 

Keywords

Cauchy numbers, Poly-Cauchy numbers, p-Cauchy numbers, Generating function, Recurrence relations

Project Number

FBA-2018-3723.

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