The Bergman kernel for intersection of two complex ellipsoids (Q2828668)

Explicit forms of the Bergman kernels of the following domains NEWLINE\[NEWLINE D_1=\big\{(z_1,z_2,z_3)\in\mathbb C^3:|z_1|^2+|z_2|^2<1,\;|z_1|^2+|z_3|^2<1\big\}, NEWLINE\]NEWLINE NEWLINENEWLINE\[NEWLINE D_2=\big\{(z_1,z_2,z_3)\in\mathbb C^3:|z_1|^6+|z_2|^2<1,\;|z_1|^6+|z_3|^2<1\big\}, NEWLINE\]NEWLINE NEWLINE\[NEWLINE D_3=\big\{(z_1,z_2,z_3)\in\mathbb C^3:|z_1|^2+|z_2|^2<1,\;|z_1|^4+|z_3|^2<|z_1|^2\big\}, NEWLINE\]NEWLINE and NEWLINENEWLINE\[NEWLINE D_4=\big\{(z_1,z_2,z_3,z_4)\in\mathbb C^4:|z_1|^2+|z_2|^2+|z_3|^2<1,\;(|z_1|^2+|z_2|^2)^2+|z_4|^2<|z_1|^2+|z_2|^2\big\} NEWLINE\]NEWLINE are given. In the proof, closed forms of some hypergeometric functions are used.