Journal of Integer Sequences, Vol. 12 (2009), Article 09.8.2

Two Formulas for Successive Derivatives and Their Applications

Grzegorz Rządkowski
Faculty of Mathematics and Natural Sciences
Cardinal Stefan Wyszyński University in Warsaw
Dewajtis 5
01 - 815 Warsaw


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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