Numerical stability of the branched continued fraction expansions of the ratios of Horn's confluent hypergeometric functions H6

Abstract

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 H6 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.