The Log-convexity of the poly-cauchy numbers

Abstract

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

Mathematics Subject Classication (2010): 05A19, 05A20, 11B83.

Key words: Cauchy numbers, poly-Cauchy numbers, multiparameter-poly-Cauchy num-
bers, log-convexity, log-concavity.