The Bergman kernel function for intersections of some cylindrical domains and Lauricella's hypergeometric function

In this paper, we show that Lauricella's hypergeometric function F-8 has a close connection with the Bergman kernel for the intersection of two cylindrical domains defined by D(P-1, P-2, P-3) := {z is an element of C-3 : vertical bar z(1)vertical bar(2p1) + vertical bar z(2)vertical bar(2p2) < 1, vertical bar z(1)vertical bar(2p1) + vertical bar z(3)vertical bar(2p3) < 1}. We investigate the boundary behavior of the Bergman kernel on the diagonal (z(1), 0, 0). We also compute the explicit form of the Bergman kernel when (P-1,P-2,P-3) = (1,P-2, P-3) and (p, 1, 1). As a consequence, we show that D(1, p(2), p(3)) is a Lu Qi-Keng domain. All results can be generalized to the intersection of cylindrical domains in any higher dimension. (C) 2021 Elsevier Inc. All rights reserved.