Quelques valeurs prises par les polynômes de Macdonald décalés. (Some special values for shifted Macdonald polynomials) (Q1288646)

In a previous paper [\textit{M. Lasalle}, J. Funct. Anal. 158, 289-324 (1998; Zbl 0914.33012)], the author defined a generalized binomial coefficient associated to the Macdonald polynomials [\textit{I.~G.~Macdonald}, Symmetric functions and Hall polynomials (Clarendon, Oxford) (1995; Zbl 0899.05068)] and gave their general properties and computed the most elementary of them. In the present paper, he computes explicitly other families of these generalized binomial coefficients, in particular those which correspond to partitions of length 2, by using the basic hypergeometric function \(_3\Phi_2\) of base \(1/q\).