Some identities of polyexponential and unipoly derangement polynomials

초록

In this paper, we introduce the poly-derangement polynomials and unipoly-derangement polynomials, and investigate their fundamental properties. In addition, we explore the relationships between these polynomials and numbers and the Stirling numbers of the first and second kinds, Bernoulli numbers, derangement numbers, Bell polynomials, and Fubini polynomials. Furthermore, for certain parameter values, we compute the numerical roots of these polynomials, examine how the roots behave as the degree increases, and present the numerical results using Mathematica. © 2026 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.