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http://dx.doi.org/10.4134/BKMS.b150502

THE BERGMAN KERNEL FOR INTERSECTION OF TWO COMPLEX ELLIPSOIDS  

Beberok, Tomasz (Department of Applied Mathematics University of Agriculture in Krakow)
Publication Information
Bulletin of the Korean Mathematical Society / v.53, no.5, 2016 , pp. 1291-1308 More about this Journal
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 intersection of two complex ellipsoids {$z{\in}\mathbb{C}^3:{\mid}z_1{\mid}^p+{\mid}z_2{\mid}^q$ < 1, ${\mid}z_1{\mid}^p+{\mid}z_3{\mid}^r$ < 1}. We consider cases p = 6, q = r = 2 and p = q = r = 2. We also investigate the Lu Qi-Keng problem for p = q = r = 2.
Keywords
Bergman kernel; Lu Qi-Keng problem; hypergeometric functions;
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Times Cited By KSCI : 1  (Citation Analysis)
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