# THE BERGMAN KERNEL FOR INTERSECTION OF TWO COMPLEX ELLIPSOIDS

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

#### 초록

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.

#### 과제정보

연구 과제 주관 기관 : Ministry of Science and Higher Education of the Republic of Poland

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