Truncation Error Bounds for Branched Continued Fraction Expansions of Some Appell’s Hypergeometric Functions F2

This paper considers the problem of approximating some Appell’s hypergeometric functions F2 by their branched continued fraction expansions. Using the formula for the difference of two approximants of a branched continued fraction, we established the truncation error bounds for such expansions. In addition, we provided another proof of the convergence of branched continued fraction expansions to the ratio of Appell’s hypergeometric functions F2. Finally, we also provide examples to demonstrate the effectiveness of branched continued fractions as a tool for approximating special functions.