Explicit Formulas of the Bergman Kernel for Some Reinhardt Domains

Abstract

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 Reinhardt domains $\{|z_3|^{\lambda } < |z_1|^{2p} + |z_2|^2, \ |z_1|^{2p} + |z_2|^2 < |z_1|^{p} \}$ and $\{|z_4|^{\lambda } < (|z_1|^2 + |z_2|^2)^{p} + |z_3|^2, \ (|z_1|^2 + |z_2|^2)^{p} + |z_3|^2 < (|z_1|^2 + |z_2|^2 )^{p/2} \}$.