Hypergeometric Reduction Formulas Involving Roots of Unity

A special F(n−1)D, with variables (ω, ω2, ..., ω(n−1)), where ω = exp(2πi/n), is expressed in terms of gamma functions. This formula is used in the proof of a reduction formula for a certain n-dimensional power series with variables (x, ωx, ω2x, ..., ωn−1x). Further generalizations of the results are established. Similar results for F(n−1)C are discussed for n ≤ 4; the general case is an open problem.