An approximation to Appell's hypergeometric function F2 by branched continued fraction

Appell's functions F-1-F-4 turned out to be particularly useful in solving a variety of problems in both pure and applied mathematics. In literature, there have been published a significant number of interesting and useful results on these functions. In this paper, we prove that the branched continued fraction, which is an expansion of ratio of hypergeometric functions F-2 with a certain set of parameters, converges uniformly to a holomorphic function of two variables on every compact subset of some domain of C-2, and that this function is an analytic continuation of such ratio in this domain. As a special case of our main result, we give the representation of hypergeometric functions F-2 by a branched continued fraction. To illustrate this, we have given some numerical experiments at the end.