Asymptotics of Diagonal Hermite–Padé Polynomials for the Collection of Exponential Functions

The asymptotics of diagonal Hermite–Padé polynomials of the first kind is studied for the system of exponential functions $\{e^{\lambda_pz}\}_{p=0}^k$, where $\lambda_0=0$ and the other $\lambda_p$ are the roots of the equation $\xi^k=1$. The theorems proved in the paper supplement the well-known results due to Borwein, Wielonsky, Stahl, Astaf'eva, and Starovoitov obtained for the case in which $\{\lambda_p\}_{p=0}^k$ are different real numbers.