On truncation error bounds of branched continued fraction expansions of some ratios of Lauricella–Saran’s hypergeometric functions F_K - Dmytryshyn, R.; Goran, V. (Matematychni Studii, 2026)
The paper considers the problem of approximating Lauricella–Saran’s hypergeometric functions F_K in special cases by branched continued fractions as a special family of functions. Under the certain conditions on the elements of branched continued fraction expansions of some ratios of these functions, it is proven that every expansion converges to the function that is analytic in the domain of analytic continuation \[D_η={zR^3z_1η, z_2η, z_30},0<η<1,\] at least as fast as a geometric series with a ratio less then unity. For this purpose, the method based on the formula for the difference of two approximants of a branched continued fraction and the PF method (based on the so-called property of fork for a branched continued fraction with positive elements) was used.