Identities of the degenerate Daehee numbers with the Bernoulli numbers of the second kind arising from nonlinear differential equation

Abstract

], Kim et al. presented some identities for the Bernoulli numbers of the second kind using differential equation. Here we use this differential equation in a different way. In this paper, we deduce some identities of the degenerate Daehee numbers with the Bernoulli numbers of the second kind of order r.

Explicit expression for symmetric identities of w-Catalan–Daehee polynomials

“…Even though the Daehee numbers are easily calculated as D n = (−1) n n! n+1 , they play important roles in connecting relationships between special numbers (see [3,5,7,9,18,[20][21][22][23][24][25]).…”

Some identities of degenerate Fubini polynomials arising from differential equations

“…After Carlitz, a group of mathematician have studied the degenerate special numbers. For example, degenerate Fubini polynomials are studied in [11], degenerated Bell polynomials in [14], degenerate Cauchy numbers in [20,21], and degenerate Daehee numbers in [16,22]. Lim studied degenerate Gennochi polynomials [17].…”

“…Recently, many mathematicians have studied special numbers using differential equations. Bernoulli numbers of the second kind are presented in [9], Frobenius-Euler polynomials are presented in [6], MittagLeffer polynomials are presented in [12], Changhee numbers and polynomials are presented in [8,10], and Daehee and degenerate Daehee numbers are presented in [16,20].…”

Degenerate Daehee Numbers of the Third Kind

“…After Carlitz [1,2], many mathematicians have studied degenerate functions and numbers (see [3,9,15,16,17,18,19,23,24]). They mainly used (1+λt) 1 λ instead of e t to degenerate polynomials and numbers.…”