The log-convexity of the poly-Cauchy numbers

TL;DR

This paper investigates the log-convexity and log-behavior of multiparameter-poly-Cauchy numbers, a generalization of Cauchy numbers, providing new insights into their mathematical properties.

Contribution

It establishes the log-convexity of multiparameter-poly-Cauchy numbers of both kinds and explores their log-behavior, advancing understanding of these generalized number sequences.

Findings

Proves log-convexity of multiparameter-poly-Cauchy numbers

Analyzes the log-behavior of these numbers

Provides theoretical results on their properties

Abstract

In 2013, Komatsu introduced the poly-Cauchy numbers, which generalize Cauchy numbers. Several generalizations of poly-Cauchy numbers have been considered since then. One particular type of generalizations is that of multiparameter-poly-Cauchy numbers. In this paper, we study the log-convexity of the multiparameter-poly-Cauchy numbers of the first kind and of the second kind. In addition, we also discuss the log-behavior of multiparameter-poly-Cauchy numbers.