A Remark on the Bergman Kernels for the Intersection of Cylindrical Hartogs Domains and Polylogarithm Functions

Abstract

In 2016, Beberok obtained an explicit formula for the Bergman kernel of a specific Reinhardt domain in ℂ³, defined by |ζ₁|²<(1−|z|²)^q,|ζ₂|²<(1−|z|²)^r where q,r>0. We derive explicit formulas for the Bergman kernels of a wider class of domains, expressed in terms of polylogarithm functions. This class includes Beberok's domain as a special case.