#####
Séminaire Lotharingien de Combinatoire, B25i (1990).

[Formerly: Publ. I.R.M.A. Strasbourg, 1991, 462/S-25, p.
83-100.]

# Serge Dulucq and Luc Favreau

# Un modèle combinatoire pour les polynômes de Bessel

**Abstract.**
We propose a combinatorial model for the Bessel polynomials. This
model, based upon weighted involutions, leads us to
combinatorial
interpretations and proofs of some identities, namely the differential
equation, recurrences of different type and the generating
exponential
function. A combinatorial proof of the orthogonality for these
polynomials and the value of the normalizing factor, using
this model, are given in a
forthcoming paper [S. Dulucq and L. Favreau, "*Combinatoire des
polynomes de Bessel. II. Orthogonalite*", Res. Resp., LaBRI,
Univ. Bordeaux I,
Talence, 1990].

The paper has been finally published under the title
"A combinatorial model for Bessel polynomials" in
*Orthogonal polynomials and their applications (Erice, 1990)*,
pp. 243-249,
IMACS Ann. Comput. Appl. Math., 9,
Baltzer, Basel, 1991.