Abstract:
We construct integral representations and asymptotic estimates for remainder terms arising in the summation of the Appell hypergeometric series $F_1$ and the related series $G_2$, which are included in Horn’s list of hypergeometric series of two variables. The obtained formulas can be used to develop algorithms for calculating $F_1$ with the help of analytic continuation formulas to the entire space $\mathbb{C}^2$. The results can find application in problems of mathematical physics and computational function theory, including in the construction of conformal mappings of complicated polygons based on the Schwarz–Christoffel integral.
Key words:Appell and Horn hypergeometric functions, analytic continuation formulas, efficient computation of hypergeometric functions.
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