TY - JOUR AU - Komatsu, Takao PY - 2019 TI - Some recurrence relations of poly-Cauchy numbers JO - Journal of Nonlinear Sciences and Applications SP - 829--845 VL - 12 IS - 12 AB - Poly-Cauchy numbers \(c_n^{(k)}\) (\(n\ge 0\), \(k\ge 1\)) have explicit expressions in terms of the Stirling numbers of the first kind. When the index is negative, there exists a different expression. However, the sequence \(\{c_n^{(-k)}\}_{n\ge 0}\) seem quite irregular for a fixed integer \(k\ge 2\). In this paper we establish a certain kind of recurrence relations among the sequence \(\{c_n^{(-k)}\}_{n\ge 0}\), analyzing the structure of poly-Cauchy numbers. We also study those of poly-Cauchy numbers of the second kind, poly-Euler numbers, and poly-Euler numbers of the second kind. Some different proofs are given. As applications, some leaping relations are shown. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.012.12.05 DO - 10.22436/jnsa.012.12.05 ID - Komatsu2019 ER -