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

摘要

In the paper, the authors elementarily unify and generalize eight identities involving the functions ±1e±t−1 and their derivatives. By one of these identities, the authors establish 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.