Estimates for the largest critical value of $T_n^{(k)}$

Nikola Naidenov, Geno Nikolov

Here we study the quantity $${\tau }_{n,k}:=\frac{|T_n^{(k)}({\omega }_{n,k})|}{T_n^{(k)}(1)},$$ where $T_n$ is the $n$-th Chebyshev polynomial of the first kind and ${\omega }_{n,k}$ is the largest…