Geodesic
An Alternative Approach to Laguerre Polynomial Identities in Combinatorics
Canadian journal of mathematics, Tome 31 (1979) no. 2, pp. 312-319

Voir la notice de l'article provenant de la source Cambridge University Press

1. In their paper “Permutation Problems and Special Functions,” Askey and Ismail [1] give the following striking identity. Consider three boxes containing j, k, m distinguishable balls, and consider all possible rearrangements of these balls such that each box still has the same number of balls; i.e., j end up in the first, k in the second, m in the third. One disregards the order of the balls within a box so there are (j + k + m)!/(j!k!m!) possible rearrangements. Let RE be the number of rearrangements where an even number of balls change boxes and R 0 the number of rearrangements where an odd number change boxes. The identity is (1.1) where (1.2) is the jth Laguerre polynomial. These polynomials are orthonormal with respect to the weight function e –x ; i.e. 
Barrett, Wayne W. An Alternative Approach to Laguerre Polynomial Identities in Combinatorics. Canadian journal of mathematics, Tome 31 (1979) no. 2, pp. 312-319. doi: 10.4153/CJM-1979-034-7
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