  I recent years, studying degenerate versions of some special polynomials,
which was initiated by Carlitz in an investigation of the degenerate Bernoulli
and Euler polynomials, regained lively interest of mant mathematicains. In this
paper, as a degenerate version of polyexponential functions introduced by
Hardy, we study degenerate polyexponential functions and derive various
properties of them. Also, we introduce new type degenerate Bell polynomials,
which are different from the previous studied partially degenerate Bell
polynomials and arise naturally in the recent study of degenerate
zero-truncated Poissonrandom variables, and deduce some of their properties.
Furthermore, we derive some identities connecting the polyexponential functions
and the new type degenerate Bell polynomials.
