%0 Book Section %1 brezinski85 %A de Sainte-Catherine, Myriam %A Viennot, Gérard %B Polynômes Orthogonaux et Applications %D 1985 %E Brezinski, Claude %E Draux, André %E Magnus, AlphonseP. %E Maroni, Pascal %E Ronveaux, André %I Springer Berlin Heidelberg %K graph.theory orthogonal polynomial spectral_graph_theory %P 120--128 %R 10.1007/BFb0076537 %T Combinatorial Interpretation of Integrals of Products of Hermite, Laguerre and Tchebycheff Polynomials %V 1171 %X Certain integrals of products of Laguerre polynomials have been interpreted as numbers of generalized derangements by Kaplansky, Even, Gillis, Jackson, Askey, Ismail, and Rashed. The analog for the Hermite polynomials have been done by Azor, Gillis, Victor, Godsil in term of matchings. Here we give a simple combinatorial (i.e. with a bijection) proof of these results. An analogous bijection is constructed for the case of Tchebycheff polynomials and leads to an interpretation with Dyck words. %@ 978-3-540-16059-5

@incollection{brezinski85, abstract = {Certain integrals of products of Laguerre polynomials have been interpreted as numbers of generalized derangements by Kaplansky, Even, Gillis, Jackson, Askey, Ismail, and Rashed. The analog for the Hermite polynomials have been done by Azor, Gillis, Victor, Godsil in term of matchings. Here we give a simple combinatorial (i.e. with a bijection) proof of these results. An analogous bijection is constructed for the case of Tchebycheff polynomials and leads to an interpretation with Dyck words.}, added-at = {2014-09-30T11:05:46.000+0200}, author = {de Sainte-Catherine, Myriam and Viennot, G\'{e}rard}, biburl = {https://www.bibsonomy.org/bibtex/27b2a150ecfce0091fd4cea0faf3e558b/ytyoun}, booktitle = {Polyn\^{o}mes Orthogonaux et Applications}, doi = {10.1007/BFb0076537}, editor = {Brezinski, Claude and Draux, André and Magnus, AlphonseP. and Maroni, Pascal and Ronveaux, André}, interhash = {0af4ea3b81e91918674b351afd3504e1}, intrahash = {7b2a150ecfce0091fd4cea0faf3e558b}, isbn = {978-3-540-16059-5}, keywords = {graph.theory orthogonal polynomial spectral_graph_theory}, language = {English}, pages = {120--128}, publisher = {Springer Berlin Heidelberg}, series = {Lecture Notes in Mathematics}, timestamp = {2016-02-25T13:26:30.000+0100}, title = {Combinatorial Interpretation of Integrals of Products of {Hermite}, {Laguerre} and {Tchebycheff} Polynomials}, volume = 1171, year = 1985 }