A Series transformation formula and related degenerate polynomials

TL;DR

This paper extends classical identities involving special functions by expressing them through degenerate power series and related degenerate polynomials, building on Bovadzhiev's recent work.

Contribution

It introduces new identities linking degenerate formal power series with various degenerate polynomials and numbers, expanding the theoretical framework.

Findings

Derived new identities involving degenerate Stirling numbers and Bell polynomials

Expressed classical formulas in terms of degenerate power series

Enhanced understanding of degenerate polynomial relationships

Abstract

Recently, Bovadzhiev studied a power series whose coefficients are binomial expressions and extended some known formulas involving classical special functions and polynomials. The aim of this paper is to adopt his ideas to express several identities involving " degenerate formal power series" as those including degenerate stirling numbers of the second kind, degenerate Bell polynomials, degenerate Fubini polynomials and degenerate poly-Bernoulli polynomials.