Degenerate Daehee Numbers of the Third Kind

Abstract

In this paper, we define new kind of Daehee numbers, the degenerate Daehee numbers of the third kind, using degenerate log function as generating function. We obtain some identities for the degenerate Daehee numbers of the third kind associated with the Daehee, degenerate Daehee and degenerate Daehee numbers of the second kind. In addition, we derive a differential equation associated with the degenerate log function. We deduce some identities from the differential equation.

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]).…”