Note on the Function F (a, b; c - n; z)

The generating function [equation] may be used to find an estimate of F(a, b; b - n; z) for large positive values of n. When the point t = 1 - 1/z lies outside the circle t = 1 the singularity t = 1 may be used to find an estimate by the method of Darboux [1] and the result is F(a, b; b - n; z) ~ 1.