A priori bounds for truncation error of branched continued fraction expansions of Horn's hypergeometric functions and their ratios

The paper considers the extension of analytic functions by a special family of functions — branched continued fractions. The truncation error bounds for branched continued fraction expansions of the Horn’s hypergeometric functions H4 and their ratios with certain conditions on real parameters are established. In this case, a new domain of analytical continuation of these functions is also established using the PF method (based on the so-called property of fork for approximants of a branched continued fraction).