Geodesic
Two formulas for successive derivatives and their applications
Journal of integer sequences, Tome 12 (2009) no. 8
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.
Classification : 11B73, 11B68
Keywords: Stirling numbers, addition formulas, generalized Euler polynomials, generalized Bernoulli polynomials 
@article{JIS_2009__12_8_a4,
     author = {Rz\k{a}dkowski,  Grzegorz},
     title = {Two formulas for successive derivatives and their applications},
     journal = {Journal of integer sequences},
     year = {2009},
     volume = {12},
     number = {8},
     zbl = {1201.11029},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2009__12_8_a4/}
}
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Rządkowski,  Grzegorz. Two formulas for successive derivatives and their applications. Journal of integer sequences, Tome 12 (2009) no. 8. http://geodesic.mathdoc.fr/item/JIS_2009__12_8_a4/