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

Appell’s functions F1–F4 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 F2 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 F2 by a branched continued fraction. To illustrate this, we have given some numerical experiments at the end.