New Properties on Degenerate Bell Polynomials

Abstract

The aim of this paper is to study the degenerate Bell numbers and polynomials which are degenerate versions of the Bell numbers and polynomials. We derive some new identities and properties of those numbers and polynomials that are associated with the degenerate Stirling numbers of both kinds.

Some identities involving degenerate Stirling numbers associated with several degenerate polynomials and numbers

“…These explorations for degenerate versons are not only limited to special polynomials and numbers but also extended to some transcendental functions, like gamma functions. In the course of this quest, many different tools are used, which include generating functions, combinatorial methods, p-adic analysis, umbral calculus, operator theory, differential equations, special functions, probability theory and analytic number theory (see [8][9][10][11][12][13][14]16] and the references therein).…”

Some identities on degenerate hyperharmonic numbers

“…These quests for degenerat versons are not only limited to special polynomials and numbers but also extended to some transcendental functions, like gamma functions (see [11]). Many different tools are used, which include generating functions, combinatorial methods, p-adic analysis, umbral calculus, operator theory, differential equations, special functions, probability theory and analytic number theory (see [8][9][10]12,14,16] and the references therein). It is also worth mentioning that λ -umbral calculus has been introduced in [8], which turns out to be more convenient than the 'classical' umbral calculus when dealing with degenerate Sheffer polynomials.…”