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 Gelʹfand, Kapranov and Zelevinsky. We construct the n distinct A-hypergeometric series solutions for each of the 2n−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.