A priori bounds for truncation error of branched continued fraction expansions of Horn's hypergeometric functions H₄ and their ratios

Key Points

Truncation error bounds are established for branched continued fractions of Horn's hypergeometric functions, highlighting their precision.
New analytical continuation domains are defined using the PF method, enhancing existing mathematical tools.
The exploration focuses on certain conditions imposed on real parameters, which are crucial for the function's behavior.
This research expands the understanding of approximation techniques within complex function theory.

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 H₄ 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).

A priori bounds for truncation error of branched continued fraction expansions of Horn's hypergeometric functions H₄ and their ratios

Key Points

Abstract

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