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  4. Numerical stability of the branched continued fraction expansions of the ratios of Horn's confluent hypergeometric functions $\mathrm{H}_{6}$

Numerical stability of the branched continued fraction expansions of the ratios of Horn's confluent hypergeometric functions $\mathrm{H}_{6}$

MMC.
2024;
Volume 11, Number 4
: pp. 1152–1166
https://doi.org/10.23939/mmc2024.04.1152
Received: May 09, 2024
Revised: November 10, 2024
Accepted: November 12, 2024

Hladun V. R., Dmytryshyn M. V., Kravtsiv V. V., Rusyn R. S.  Numerical stability of the branched continued fraction expansions of the ratios of Horn's confluent hypergeometric functions $\mathrm{H}_{6}$.  Mathematical Modeling and Computing. Vol. 11, No. 4, pp. 1152–1166 (2024)

Authors:
  1. V. R. Hladun
  2. M. V. Dmytryshyn
  3. V. V. Kravtsiv
  4. R. S. Rusyn
1
Lviv Polytechnic National University
2
West Ukrainian National University
3
Vasyl Stefanyk Precarpathian National University
4
Vasyl Stefanyk Precarpathian National University

The paper establishes the conditions of numerical stability of a numerical branched continued fraction using a new method of estimating the relative errors of the computing of approximants using a backward recurrence algorithm.  Based this, the domain of numerical stability of branched continued fractions, which are expansions of Horn's confluent hypergeometric functions $\mathrm{H}_{6} $ with real parameters, is constructed.  In addition, the behavior of the relative errors of computing the approximants of branched continued fraction using the backward recurrence algorithm and the algorithm of continuants was experimentally investigated.  The obtained results illustrate the numerical stability of the backward recurrence algorithm.

branched continued fraction
Horn hypergeometric function
numerical approximation
roundoff error
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