Sums of products of ultraspherical functions.

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]