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Abstract: We introduce a -analogue of Wigner’s 9- symbols following the notational scheme used by Wilson in identifying the 6- symbols with Racah polynomials, which eventually led Askey and Wilson to obtain a -analogue of them, namely, the -Racah polynomials. Most importantly, we prove the orthogonality of our analogues in complete generality, as well as derive an explicit polynomial expression for these new functions. [Copyright &y& Elsevier]

Analytical expressions for the sum Σ[sup ∞, sub n=0] (n + λ)[Γ(n + 1)Γ(n + 2λ)]² × C[sup λ, sub n](x)C[sup λ, sub n](y)C[sup λ, sub n](z)D[sup λ, sub n](u) are given, where C[sup λ, sub n] are ultraspherical polynomials and functions of the second kind, respectively, on the sets {x,y,z <1, u > 1} and {x,y,z,u < 1}. [ABSTRACT FROM AUTHOR]