Analytic Continuation of Appell's Hypergeometric Series F2 to the Vicinity of the Singular Point x = 1, y = 1

Abstract

The infinite series, absolutely convergent if |x| + |y| < 1, for Appell's F2 (α, β, β′, γ, γ′; x, y) is analytically continued into a linear combination of four infinite series in powers of (x - 1) and (y - 1); each of the latter four series is absolutely convergent if |x − 1| + |y − 1| < 1. The analytic continuation is carried out by manipulation of the Mellin-Barnes integral representations for the hypergeometric functions appearing in the course of the calculation.