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

Geno Nikolov, Nikola Naidenov, Alexei Shadrin

We study the quantity $${\tau }_{n,k}:=\frac{|T_n^{(k)}({\omega }_{n,k})|}{T_n^{(k)}(1)},$$ where $T_n$ is the Chebyshev polynomial of degree $n$, and ${\omega }_{n,k}$ is the rightmost zero of $T_n…