The Log-convexity of Some Sequences Related to Cauchy Numbers of Two Kinds

Abstract

For Cauchy numbers of the first kind $\{a_n\}n\ge 0$ and Cauchy numbers of the second kind $\{b_n\}n\ge 0$, this paper focuses on the log-convexity of some sequences related to $\{a_n\}n\ge 0$ and $\{b_n\}n\ge 0$. For example, we discuss log-convexity of $\{n|a_n|–|a_{n+1}|\}n\ge 1$, $\{bn+1–n{b}_n\}n\ge 1$, $\{n|a_n|\}n\ge 1$, and $\{(n+1)b_n{\}}_{n\ge 0}$. In addition, we investigate log-balancedness of some sequences involving $a_n$ (or $b_n$).