A Series transformation formula and related degenerate polynomials

Abstract

Recently, Boyadzhiev 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. 2010 Mathematics Subject Classification. 11B83; 05A15. Key words and phrases. degenerate power series; degenerate Stirling numbers of the first kind; degenerate Stirling numbers of the second kind; degenerate Bell polynomials; degenerate Fubini polynomials; degenerate poly-Bernoulli polynomials.