On convergence of function F4(1,2;2,2;z1,z2) expansion into a branched continued fraction
In the paper, the possibility of the Appell hypergeometric function ${F_4}(1,2; 2,2;{z_1},{z_2})$ approximation by a branched continued fraction of a special form is analysed. The correspondence of the constructed branched continued fraction to the Appell hypergeometric function $F_4$ is proved. The convergence of the obtained branched continued fraction in some polycircular domain of two-dimensional complex space is established, and numerical experiments are carried out. The results of the calculations confirmed the efficiency of approximating the Appell hypergeomet