The Combinatorics of Laguerre, Charlier, and Hermite Polynomials
- 1 February 1989
- journal article
- research article
- Published by Wiley in Studies in Applied Mathematics
- Vol. 80 (1) , 25-36
- https://doi.org/10.1002/sapm198980125
Abstract
This paper describes several combinatorial models for Laguerre, Charlier, and Hermite polynomials, and uses them to prove combinatorially some classical formulas. The so‐called “Italian limit formula” (from Laguerre to Hermite), the Appel identity for Hermite polynomials, and the two Sheffer identities for Laguerre and Charlier polynomials are proved. We also give bijective proofs of the three‐term recurrences. These three families form the bottom triangle in R. Askey's chart classifying hypergeometric orthogonal polynomials.Keywords
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