Several explicit formulas for (degenerate) Narumi and Cauchy polynomials and numbers

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Qi F., Daǧll M. C., Lim D.

Open Mathematics, vol.19, no.1, pp.833-849, 2021 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 19 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.1515/math-2021-0079
  • Journal Name: Open Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.833-849
  • Keywords: Bell polynomial of the second kind, Cauchy number, degenerate Cauchy number, explicit formula, Faà di Bruno formula, generating function, Narumi number, Narumi polynomial
  • Akdeniz University Affiliated: Yes

Abstract

© 2021 Feng Qi et al., published by De Gruyter 2021.In this paper, with the aid of the Faà di Bruno formula and by virtue of properties of the Bell polynomials of the second kind, the authors define a kind of notion of degenerate Narumi numbers and polynomials, establish explicit formulas for degenerate Narumi numbers and polynomials, and derive explicit formulas for the Narumi numbers and polynomials and for (degenerate) Cauchy numbers.