Abstract:
We construct the beta function of the Hermitian symmetric space $\mathrm O(n,2)/\mathrm O(n)\times\mathrm O(2)$, or, equivalently, of the tube $(\operatorname{Re}z_0)^2> (\operatorname{Re}z_1)^2+\dots+(\operatorname{Re}z_n)^2$ in $\mathbb C^{n+1}$. Bibl. 11 titles.
Key words and phrases:beta integrals, Berezin kernels, Cartan domains, Lie ball, Hua integrals, tube domains, Hermitian symmetric spaces.