Asymptotics of diagonal Hermite–Padé polynomials for the collection of exponential functions

Abstract

The asymptotics of diagonal Hermite–Padé polynomials of the first kind is studied for the system of exponential functions \(\left\{ {{e^{{\lambda _p}z}}} \right\}_{p = 0}^k\), where λ₀ = 0 and the other λ_p are the roots of the equation ξ^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 {λ_p}_p=0^k are different real numbers.