Some identities on degenerate Bell polynomials and their related identities

TL;DR

This paper explores identities involving degenerate Bell polynomials, establishing relationships between different types through series transformation formulas, thereby advancing understanding of their structural properties.

Contribution

It introduces new identities for degenerate Bell polynomials and clarifies the relationship between two different types using series transformation techniques.

Findings

Derived new identities for degenerate Bell polynomials

Established connections between different types of degenerate Bell polynomials

Utilized series transformation formulas to prove identities

Abstract

Recently, several types of degenerate Bell polynomials have been introduced as degenerate versions of the ordinary Bell polynomials. The aim of this paper is to study some identities for the degenerate Bell polynomials and their related identities by making use of series transformation formula obtained by Boyadzhiev. In particular, this answers to the natural question about the relationship between two different types of degenerate Bell polynomials.