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THE BERGMAN KERNEL FOR INTERSECTION OF TWO COMPLEX ELLIPSOIDS

2016
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Bulletin of the Korean Mathematical Society
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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 ∈ C 3 : |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. in [18] compute Bergman kernel for nonhomogeneous domain for any positive integers q 1 and q 2 . The goal of this paper is

doi:10.4134/bkms.b150502
fatcat:ceeyk24isre7phphmggu2jaz34