A Generalized Hypergeometric Function II. Asymptotics and D4 Symmetry.

In previous work we introduced and studied a function R(a₊, a_{_}, c; v, &vcaron;) that generalizes the hypergeometric function. In this paper we focus on a similarity-transformed function ε (a₊, a_{_}, γ; v, &vcaron;), with parameters γ ∈ C⁴ related to the couplings c ∈ C⁴ by a shift depending on a₊, a_{_}. We show that the ε-function is invariant under all maps γ → w(γ), with w in the Weyl group of type D₄. Choosing a₊, a_{_} positive and y, &vcaron; real, we obtain detailed information on the ¦Re v¦ → ∞ asymptotics of the ε-function. In particular, we explicitly determine the leading asymptotics in terms of plane waves and the c-function that implements the similarity R → &epsilon. [ABSTRACT FROM AUTHOR]