paper

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

Bai-Ni Guo, Feng Qi

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

Name: Explicit formulae for computing Euler polynomials in terms of Stirling numbers of the second kind
Author: Bai-Ni Guo, Feng Qi

Bai-Ni Guo, Feng Qi

paper2013-10-19English

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Description

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.