#####
Séminaire Lotharingien de Combinatoire, B08c (1984), 9
pp.

[Formerly: Publ. I.R.M.A. Strasbourg, 1984, 229/S-08, p.
17-25.]

# Dominique Foata and Doron Zeilberger

# Weighted Derangements and Laguerre Polynomials

**Abstract.**
The integral of a product of finitely many generalized
Laguerre polynomials with respect to their weight function
is expressed as the generating polynomial for so-called
(*a*,*b*,...,*d*)-derangements by their numbers of cycles. The positivity
of the integral is a consequence of this combinatorial
interpretation.

The present paper has been completed
and updated to become:

Dominique Foata and Doron Zeilberger,
Laguerre polynomials, weighted derangements
and positivity, SIAM J. Discrete Math., vol. 1, 1988,
p. 425--433.
The following versions are available: