The paper investigates the numerical stability of branched continued fraction expansions of Appell hypergeometric functions F₂ and their ratios in special cases. This is important when computing the values of these special functions, as they are widely used in science and engineering. Using the proposed new approach for estimating the so-called tails of approximants of branched continued fraction, we established the sets of numerical stability of the above-mentioned expansions in the cases of real and complex elements. Numerical experiments presented at the end confirm the obtained theoretical results.
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Roman Dmytryshyn (2026) studied this question.
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