Abstract: E=E(m,n,k)={(z,w)∈C^n+m:|z|²+|w|^2k<1,z∈Cⁿ,w∈C^m,k>0} is a class of pseudoconvex domains in C^n+m. In this note is showed it, that lim_(z,w)→∂EJ_E((z,w))=π^n+m(n+m+1)ⁿ/(n+m)!,when m>1. lim_(z,w)→∂EJ_E((z,w))=πⁿ⁺¹(n+2)ⁿ⁺¹/(n+1)!, when m=1 holds on the strongly pseudoconvex points of boundary ∂E; the limit given above not exist on the weakly pseudoconvex points of boundary ∂E.

Key words: Pseudoconvex domain, Holomorphic invariant, Bergman kernel function