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Two Formulas for Successive Derivatives and Their Applications
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Grzegorz Rządkowski

Faculty of Mathematics and Natural Sciences

Cardinal Stefan Wyszyński University in Warsaw

Dewajtis 5

01 - 815 Warsaw

Poland

**Abstract:**

We recall two formulas, due to C. Jordan, for the
successive derivatives of functions with an exponential or logarithmic
inner function. We apply them to get addition formulas for the Stirling
numbers of the second kind and for the Stirling numbers of the first
kind. Then we show how one can obtain, in a simple way, explicit
formulas for the generalized Euler polynomials, generalized Euler
numbers, generalized Bernoulli polynomials and the Bell polynomials.

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(Concerned with sequences
A008275
A008277
A008292.)

Received May 8 2009;
revised version received November 12 2009.
Published in *Journal of Integer Sequences*, November 16 2009.

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