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

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

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 expl...

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Veröffentlicht in:Open mathematics (Warsaw, Poland) Poland), 2021-08, Vol.19 (1), p.833-849
Hauptverfasser: Qi, Feng, Dağlı, Muhammet Cihat, Lim, Dongkyu
Format: Artikel
Sprache:eng
Schlagworte:
11B83
11C08
33B10
Bell polynomial of the second kind
Cauchy number
Combinatorial analysis
degenerate Cauchy number
explicit formula
Faà di Bruno formula
generating function
Narumi number
Narumi polynomial
Polynomials
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Zusammenfassung: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.
ISSN:2391-5455
2391-5455
DOI:10.1515/math-2021-0079