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

Abstract

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.

Keywords

• narumi number
• narumi polynomial
• cauchy number
• degenerate cauchy number
• explicit formula
• bell polynomial of the second kind
• faà di bruno formula
• generating function
• 11b83
• 11c08
• 33b10