Asymptotics of the type II Hermite–Padé approximation of exponential functions with complex multipliers in the exponent

The asymptotic behavior of diagonal Hermite–Padé polynomials and diagonal Hermite–Padé approximations of type II for the system of exponentials $\{e^{\lambda_pz}\}_{p=0}^k$ in which $\lambda_0=0$, while the rest $\lambda_p$ are the roots of the equation $\xi^k=1$ is determined. The theorems complement known results of H. Padé, D. Braess, A. I. Aptekarev, H. Stahl, F. Wielonsky, W. Van Assche, A. B. J. Kuijlaars, A. P. Starovoitov, obtained for the case, where the $\{\lambda_p\}_{p=0}^k$ — different real numbers.