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