Explicit formulae for computing Euler polynomials in terms of Stirling numbers of the second kind

Bai-Ni Guo, Feng Qi

Published 2013-10-19, updated 2014-05-21Version 2

In the paper, the author elementarily unifies and generalizes eight identities involving the functions $\frac{\pm1}{e^{\pm t}-1}$ and their derivatives. By one of these identities, the author establishes two explicit formulae for computing Euler polynomials and two-parameter Euler polynomials, which are a newly introduced notion, in terms of Stirling numbers of the second kind.