Gauss hypergeometric functions with a dihedral monodromy group can be
expressed as elementary functions, since their hypergeometric equations can be
transformed to Fuchsian equations with cyclic monodromy groups by a quadratic
change of the argument variable. The paper presents general elementary
expressions of these dihedral hypergeometric functions, involving finite
bivariate sums expressible as terminating Appell's F2 or F3 series.
Additionally, trigonometric expressions for the dihedral functions are
presented, and degenerate cases (logarithmic, or with the monodromy group Z/2Z)
are considered.Comment: 28 pages; trigonometric expressions added; transformations and
invariants moved to arxiv.org/1101.368
