Submitted for publication, read at the conference
"Leonhard Euler, mathématicien, physicien et théoricien
de la musique," IRMA Strasbourg, november 15-16, 2007, X. Hascher and
A. Papadopoulos, org.
LES POLYNOMES EULERIENS, D'EULER A CARLITZ
The polynomials commonly called "Eulerian" today have been
introduced by Euler himself in his famous book "Institutiones calculi
differentialis cum eius usu in analysi finitorum ac Doctrina serierum"
(chap. VII), back in 1755. They have been since thoroughly studied,
extended, applied. The purpose of the present paper is to go back to
Euler's memoir, find out his motivation and reproduce his derivation,
surprisingly partially forgotten. The rebirth of those polynomials in a
q-environment is due to Carlitz two centuries after Euler. A brief
overview of Carlitz's method is given, as well as a contemporary
application of those q-polynomials.
foata at math dot u-strasbg dot fr
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