On singular univariate specializations of bivariate hypergeometric functions
arXiv:0906.1861 · doi:10.1016/j.jmaa.2009.10.018
Abstract
It is tempting to evaluate F2(x,1) and similar univariate specializations of Appell's 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 on concrete examples.
10 pages