Best weighted approximation of some kernels on the real axis

We calculate the exact value and find the polynomial of the best weighted polynomial approximation of kernels of the form $\frac {A+Bt}{(t^2+λ^2)^{s+1}}$, where $A$ and $B$ are fixed complex numbers, $λ>0$, $s\in {\mathbb N}$, in the mean square metric.