Bull. Korean Math. Soc. 2016; 53(5): 1427-1437
Online first article August 25, 2016 Printed September 30, 2016
https://doi.org/10.4134/BKMS.b150736
Copyright © The Korean Mathematical Society.
Joohee Jeong and Seog-Hoon Rim
Kyungpook National University, Kyungpook National University
Cauchy polynomials are also called Bernoulli polynomials of the second kind and these polynomials are very important to study mathematical physics. D. S. Kim et al. have studied some properties of Bernoulli polynomials of the second kind associated with special polynomials arising from umbral calculus. T. Kim introduced the degenerate Cauchy numbers and polynomials which are derived from the degenerate function $e^t$. Recently J. Jeong, S. H. Rim and B. M. Kim studied on finite times degenerate Cauchy numbers and polynomials. In this paper we consider finite times degenerate higher-order Cauchy numbers and polynomials, and give some identities and properties of these polynomials.
Keywords: higher-order Cauchy numbers, higher-order degenerate Cauchy polynomials, $k$-times degenerate higher-order Cauchy polynomials, higher order Bernoulli polynomials
MSC numbers: 11B68, 11S40, 11S80
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