On Some Branched Continued Fraction Expansions for Horn’s Hypergeometric Function H4(a,b;c,d;z1,z2) Ratios

The paper deals with the problem of representation Horn’s hypergeometric functions by branched continued fractions. formal fraction expansions for three different function H4 ratios are constructed. method employed is a two-dimensional generalization classical constructing Gaussian fraction. It proven that fraction, which an expansion one ratios, uniformly converges to holomorphic two variables on every compact subset some domain H,H⊂C2, and this analytic continuation ratio in H. application approximation associated double series considered, expression solutions systems partial differential equations indicated.