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

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Abstract

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.

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Eight interesting identities involving the exponential function, derivatives, and Stirling numbers of the second kind

Feng Qi (2012)

In the paper, the author establishes some identities which show that the functions \(\frac1{(1-e^{\pm t})^k}\) and the derivatives \(\bigl(\frac1{e^{\pm t}-1}\bigr)^{(i)}\) can be expressed each other by linear combinations with coefficients involving the combinatorial numbers and the Stirling numbers of the second kind, where \(t\ne0\) and \(i,k\in\mathbb{N}\).

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Explicit formulas for computing Bernoulli numbers of the second kind and Stirling numbers of the first kind

Feng Qi (2013)

In the paper, by establishing a new and explicit formula for computing the \(n\)-th derivative of the reciprocal of the logarithmic function, the author presents new and explicit formulas for calculating Bernoulli numbers of the second kind and Stirling numbers of the first kind. As consequences of these formulas, a recursion for Stirling numbers of the first kind and a new representation of the reciprocal of the factorial \(n!\) are derived. Finally, the author finds several identities and integral representations relating to Stirling numbers of the first kind.