Truncation error bounds of branched continued fraction expansions of special ratios of Horn's hypergeometric functions \(H_4\)
DOI:
https://doi.org/10.64700/altay.15Keywords:
hypergeometric function, branched continued fraction, approximation by rational functions, rate of convergence, analytic continuationAbstract
The paper considers the branched continued fraction extensions of special ratios of Horn's hypergeometric functions \(H_4\) with real parameters and variables. Truncation error bounds are established for such expansions with certain conditions on their coefficients. Some domains of analytical continuation of the above-mentioned special ratios are 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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Copyright (c) 2025 Roman Dmytryshyn, Clemente Cesarano, Ilona-Anna Lutsiv
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