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.