Bulletin of the
Korean Mathematical Society BKMS

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 $\{z \in \mathbb{C}^3 \colon |z_1|^p + |z_2|^q < 1$, $|z_1|^p + |z_3|^r < 1\}$. 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

MSC numbers: Primary 32A25; Secondary 33D70