On singular univariate specializations of bivariate hypergeometric functions

It is tempting to evaluate F 2 ( x , 1 ) and similar univariate specializations of Appellʹs functions by evaluating the apparent power series at x = 0 straight away using the Gauss formula for 2F1(1). But this kind of naive evaluation can lead to errors as the 2F1(1) coefficients might eventually diverge; then the actual power series at x = 0 might involve branching terms. This paper demonstrates these complications by concrete examples.