The Largest Entry in the Inverse of a Vandermonde Matrix

We investigate the size of the largest entry (in absolute value) in the inverse of certain Vandermonde matrices. More precisely, for every real $b > 1$,let$M_b(n)$ be the maximum of the absolute values of the entries of the inverse of the $n\times n$ matrix $[b^{ij}{]}_{0\le i,j<n}$. We prove that ${\lim }_{n\to +\mathrm{\infty }}{M}_b(n)$ exists, and we provide some formulas for it.