A priori bounds for truncation error of branched continued fraction expansions of Horn's hypergeometric functions $$$H_4$$$ and their ratios

R.I. Dmytryshyn; C. Cesarano; M. Dmytryshyn; I.-A.V. Lutsiv

doi:10.15421/242502

A priori bounds for truncation error of branched continued fraction expansions of Horn's hypergeometric functions $$$H_4$$$ and their ratios

R.I. Dmytryshyn (Vasyl Stefanyk Precarpathian National University), https://orcid.org/0000-0003-2845-0137
C. Cesarano (International Telematic University UNINETTUNO), https://orcid.org/0000-0002-1694-7907
M. Dmytryshyn (West Ukrainian National University), https://orcid.org/0000-0002-0609-9764
I.-A.V. Lutsiv (Vasyl Stefanyk Precarpathian National University), https://orcid.org/0000-0002-4100-2972

Abstract

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 $$$H_4$$$ 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).

Keywords

hypergeometric function; branched continued fraction; analytic functions; approximation by rational functions; convergence; rate of convergence; analytic continuation

MSC 2020

33C65; 32A17; 41A20; 32A10; 40A99; 41A25; 30B40

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References

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