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 $\{ |z_3|^{ \lambda} < |z_1|^{ 2p} + |z_2|^2, \quad |z_1|^{ 2p} + |z_2|^2 < |z_1|^{ p} \}$ and $\{ |z_4|^{ \lambda} < (|z_1|^2 + |z_2|^2)^{ p} + |z_3|^2, \quad (|z_1|^2 + |z_2|^2)^{ p} + |z_3|^2 < (|z_1|^2 + |z_2|^2 )^{ p/2} \}$.
Categories: math.CV