Geodesic
Weighted Derangements and Laguerre Polynomials
Séminaire lotharingien de combinatoire, Tome 08 (1983)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

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. 
@article{SLC_1983_08_a2,
     author = {Dominique Foata and Doron Zeilberger},
     title = {Weighted {Derangements} and {Laguerre} {Polynomials}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {08},
     year = {1983},
     url = {http://geodesic.mathdoc.fr/item/SLC_1983_08_a2/}
}
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AU  - Dominique Foata
AU  - Doron Zeilberger
TI  - Weighted Derangements and Laguerre Polynomials
JO  - Séminaire lotharingien de combinatoire
PY  - 1983
VL  - 08
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_1983_08_a2/
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%A Doron Zeilberger
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%I mathdoc
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Dominique Foata; Doron Zeilberger. Weighted Derangements and Laguerre Polynomials. Séminaire lotharingien de combinatoire, Tome 08 (1983). http://geodesic.mathdoc.fr/item/SLC_1983_08_a2/