On finite-times degenerate Cauchy numbers and polynomials

• Published in: Advances in difference equations Vol. 2015; no. 1; pp. 1 - 12
• Main Authors: Jeong, Joohee, Rim, Seog-Hoon, Kim, Byung Moon
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 16.10.2015; Springer Nature B.V
• Subjects: Analysis; Calculus; Difference and Functional Equations; Difference equations; Functional Analysis; Functions (mathematics); Mathematical analysis; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Partial Differential Equations; Polynomials; Recent Developments in Difference Equations; Texts; degenerate Cauchy polynomials; 11S80; higher order Bernoulli polynomials; 11S40; times degenerate Cauchy polynomials; 11B68; Cauchy numbers
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/s13662-015-0663-8

Cauchy polynomials are also called Bernoulli polynomials of the second kind and these polynomials are very important to study mathematical physics. Kim et al. have studied some properties of Bernoulli polynomials of the second kind associated with special polynomials arising from umbral calculus. Kim introduced the degenerate Cauchy numbers and polynomials which are derived from the degenerate function e t . In this paper, we try to degenerate Cauchy numbers and polynomials k -times and investigate some properties of these k -times degenerate Cauchy numbers and polynomials.