Solving algebraic equations in terms of A-hypergeometric series

The roots of the general equation of degree n satisfy an A-hypergeometric system of differential equations in the sense of Gel'fand, Kapranov and Zelevinsky. We construct the n distinct A-hypergeometric series solutions for each of the 2(n-1) triangulations of the Newton segment. This works over any field whose characteristic is relatively prime to the lengths of the segments in the triangulation. (C) 2000 Elsevier Science B.V. All rights reserved.