FPM 1998, vol. 4, no. 2, pp. 669-689

FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(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 $(1,1)$ 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 $$ j\mapsto -j-1
$$ , $j ∈$ Z, and they correlate between each other.

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Representations for Appell's series F2(x,y) to the vicinity of the singular point (1,1) and near the boundary of its domain of convergence

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