Degenerate polyexponential functions and degenerate Bell polynomials

• Published in: Journal of mathematical analysis and applications Vol. 487; no. 2; p. 124017
• Main Authors: Kim, Taekyun, Kim, Dae San
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.07.2020
• Subjects: Degenerate Hurwitz zeta function; Degenerate Lerch zeta function; Degenerate polyexponential function; Degenerate Riemann zeta function; New type degenerate Bell polynomial; Degenerate polyexponential function; Degenerate Hurwitz zeta function; Degenerate Lerch zeta function; New type degenerate Bell polynomial; Degenerate Riemann zeta function
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2020.124017

In 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 many mathematicians. 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 previously studied partially degenerate Bell polynomials and arise naturally in the recent study of degenerate zero-truncated Poisson random variables, and deduce some of their properties. Furthermore, we derive some identities connecting the polyexponential functions and the new type degenerate Bell polynomials.