SOME RELATIONSHIPS BETWEEN POLY-CAUCHY TYPE NUMBERS AND POLY-BERNOULLI TYPE NUMBERS

T. Komatsu; K´alm´an Liptai; L´aszl´o Szalay

T. Komatsu
K´alm´an Liptai
L´aszl´o Szalay

Keywords: poly-Cauchy numbers, poly-Bernoulli numbers, poly-Cauchy type numbers, poly-Bernoulli type numbers, Cauchy numbers, Bernoulli numbers

Abstract

In this paper, we show some relationships between poly-Cauchy type numbers and poly-Bernoulli type numbers. Poly-Cauchy type numbers include poly-Cauchy numbers introduced by T. Komatsu, and poly-Bernoulli type numbers include poly-Bernoulli numbers introduced by M. Kaneko. Both numbers are generalizations of classical Cauchy numbers and classical Bernoulli numbers, respectively.