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Combinatorial interpretation of integrals of products of hermite, Laguerre and Tchebycheff polynomials

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Polynômes Orthogonaux et Applications

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1171))

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.

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References

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Author information

Authors and Affiliations

  1. U.E.R. de Mathématiques et Informatique, Université de Bordeaux I, 33405, Talence, France

    Myriam de Sainte-Catherine & Gérard Viennot

Authors
  1. Myriam de Sainte-Catherine
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  2. Gérard Viennot
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Editor information

Claude Brezinski André Draux Alphonse P. Magnus Pascal Maroni André Ronveaux

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© 1985 Springer-Verlag

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de Sainte-Catherine, M., Viennot, G. (1985). Combinatorial interpretation of integrals of products of hermite, Laguerre and Tchebycheff polynomials. In: Brezinski, C., Draux, A., Magnus, A.P., Maroni, P., Ronveaux, A. (eds) Polynômes Orthogonaux et Applications. Lecture Notes in Mathematics, vol 1171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076537

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  • DOI: https://doi.org/10.1007/BFb0076537

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16059-5

  • Online ISBN: 978-3-540-39743-4

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