A note on the Lie ball (Q2739301)

Let \(B\) be the unit ball in \(\mathbb{R}^n\). Then the Lie ball \(L=\{z \in \mathbb{C}^n:L(z) <1\}\) is the harmonic envelope of holomorphy of \(B\) (that is, \(L\) is the maximal domain in \(\mathbb{C}^n\) containing \(B\) such that every function \(h\) harmonic on \(B\) can be extended as a holomorphic function on \(L)\). Now to find the domain of convergence of Taylor expansions of all \(h\) at 0, one can deal with the problem of finding the largest \(n\)-circled domain contained in the Lie ball. Actually the latter domains is \(\{z\in \mathbb{C}^n: H(z)<1\}\). This note presents an effective formula for \(H(z)\).