(FUNDAMENTAL AND APPLIED MATHEMATICS)

1998, VOLUME 4, NUMBER 2, PAGES 669-689

## Representations for Appell's series $F$2(x,y) to the vicinity of the singular point $\left(1,1\right)$ and near the boundary of its domain of convergence

V. F. Tarasov

Abstract

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 Exact analytical representations for Appell's series $F_2(x,y)$ to the vicinity of the singular point $(1,1)$ and the boundary of its domain of convergence are given. It is shown, that Appell's functions $F_2(1,1)$ and $F_3(1,1)$ have the property of mirror-like symmetry with respect to the center $j_0=-1/2$ under the change $j\mapsto -j-1$, $j\in\mathbb{Z}$, and they correlate between each other. 

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