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

Key Points

• The aim is to extend the understanding of Bergman kernels for a broader class of cylindrical Hartogs domains.
• Derived explicit formulas for Bergman kernels.
• Explored the relationships with polylogarithm functions.
• Included specific Reinhardt domains as special cases.
• Established formulas for Bergman kernels in a wider class of domains.
• Included previous findings from Beberok's research as a subset.
• Showed connections between these kernels and polylogarithm functions.