Estimation of the remainder terms of certain Horn hypergeometric series (Q6661386)

The authors develop an algorithm for computing the Appell hypergeometric series \(F_1\), as well as some other analytic continuation formulas. They also obtain an effective method for estimating and calculating the remainder of summation of certain series which are included in Horn's list of hypergeometric series of two variables. They present certain relations and a theorem to derive such integral representations and asymptotics.