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THE BERGMAN KERNEL FOR INTERSECTION OF TWO COMPLEX ELLIPSOIDS

  • Beberok, Tomasz (Department of Applied Mathematics University of Agriculture in Krakow)
  • Received : 2015.06.25
  • Published : 2016.09.30

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.

Acknowledgement

Supported by : Ministry of Science and Higher Education of the Republic of Poland

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