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NEW PROPERTIES OF THE P. E. APPELL HYPERGEOMETRIC SERIES F₂(α;β, β′;γ, γ′;x, y) TO THE VICINITY OF THE SINGULAR POINT (1, 1) AND NEAR THE BOUNDARY OF ITS DOMAIN OF CONVERGENCE D₂:|x|+|y|<1

V. F. TARASOV

Department of Mathematics, Technical University of Bryansk, 241035, Russia

https://doi.org/10.1142/S0217979210056505Cited by:10 (Source: Crossref)

Abstract

Exact analytical 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 are given. It is shown that Appell's functions F₂(1, 1) and F₃(1, 1) have the property of mirror-like symmetry with respect to the center j₀ ↦ -(1/2) under the change j ↦ -j-1, z∈ℤ, and they correlate between each other.

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