• Title, Summary, Keyword: Lu Qi-Keng problem

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THE BERGMAN KERNEL FOR INTERSECTION OF TWO COMPLEX ELLIPSOIDS

  • Beberok, Tomasz
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.5
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    • pp.1291-1308
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    • 2016
  • 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.