Two formulas for successive derivatives and their applications
J. Integer Seq. 12(8), Article ID 09.8.2, 11 p., electronic only (2009)
Summary
Summary: 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.
