Abstract:
Integral representations and estimates for the remainder term for the summation of the double hypergeometric Appell series $F_2$ are constructed. The resulting formulas have applications in developing algorithms for computing the Appell functions $F_1$ and $F_3$ in $\mathbb{C}^2$ using analytic continuation formulas. The results have applications to problems in mathematical physics and computational function theory, including the construction of conformal mappings of complicated polygons based on the Christoffel–Schwarz integral.
Key words:Appell hypergeometric functions, analytic continuation formulas, efficient computation of hypergeometric functions, estimations of the remainder terms of the hypergeometric series.
