Analysis establishes truncation error bounds in branched continued fractions of Horn's hypergeometric functions, suggesting new domains for analytical continuation.
The paper considers the extension of analytic functions by a special family of functions — branched continued fractions. The truncation error bounds for branched continue 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).
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Dmytryshyn et al. (2025) studied this question.
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