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


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.


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


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