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A Generalized Hypergeometric Function II. Asymptotics and D4 Symmetry.
- Source :
- Communications in Mathematical Physics; Dec2003, Vol. 243 Issue 3, p389-412, 24p
- Publication Year :
- 2003
-
Abstract
- In previous work we introduced and studied a function R(a<subscript>+</subscript>, a<subscript>_</subscript>, c; v, &vcaron;) that generalizes the hypergeometric function. In this paper we focus on a similarity-transformed function ε (a<subscript>+</subscript>, a<subscript>_</subscript>, γ; v, &vcaron;), with parameters γ ∈ C<superscript>4</superscript> related to the couplings c ∈ C<superscript>4</superscript> by a shift depending on a<subscript>+</subscript>, a<subscript>_</subscript>. We show that the ε-function is invariant under all maps γ → w(γ), with w in the Weyl group of type D<subscript>4</subscript>. Choosing a<subscript>+</subscript>, a<subscript>_</subscript> 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]
Details
- Language :
- English
- ISSN :
- 00103616
- Volume :
- 243
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Communications in Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 16794128
- Full Text :
- https://doi.org/10.1007/s00220-003-0969-3