The generalized Koebe function

We observe that the extremal function for $|a_{3}|$ within the class $U'_{\alpha}$ (see Starkov [1]) has as well the property that max $|A_{4}|>4.15$, if $\alpha=2$. The problem is equivalent to the global estimate for Meixner-Pollaczek polynomials $P^{1}_{3}(x;\theta)$.