On the Numerical Stability of Fractional Expansions of Triple Hypergeometric Functions $F_K$ in Special Cases

Source abstract

The paper studies the numerical stability of branched continued fractions that represent expansions of triple hypergeometric functions FK with real parameters in special cases. Using a new method for estimating the relative errors of computing approximants via a backward recurrence algorithm, we establish the domain of numerical stability for these branched continued fractions. Additionally, the behavior of the relative errors in computing the approximants of the branched continued fractions using this algorithm was experimentally investigated. Numerical experiments confirm the obtained theoretical results.