Explicit formulas of the Bergman kernel for some Reinhardt domains

2015/07/21 by Beberok, Tomasz
#32A25 #33D70 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1507.05879

Abstract

In this paper we obtain the closed forms of some hypergeometric functions. As an application, we obtain the explicit forms of the Bergman kernel functions for Reinhardt domains \|z₃|^λ < |z₁|^2p + |z₂|², |z₁|^2p + |z₂|² < |z₁|^p \ and \|z₄|^λ < (|z₁|² + |z₂|²)^p + |z₃|², (|z₁|² + |z₂|²)^p + |z₃|² < (|z₁|² + |z₂|² )^p/2 \.

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