The Bergman Kernel of Complex Ovals and Multivariable Hypergeometric Functions

We compute explicitly the Bergman and Szegő kernels for a class of pseudoconvex domains. The kernels are expressed in terms of Appellʹs multivariable hypergeometric functions. These explicit formulas are applied to investigate the asymptotic behavior of the Bergman kernel near some weakly pseudoconvex boundary points.