depend only on $\max \{|s_m|\}$. From the point of view of the interpolation problem, this corresponds to the fact that we get a new regularly solvable problem of the form (\[2n-interpolation\]) (and (\[SRS\])), where $f$ is exchanged for a new varied function $\tilde f$ such that $\tilde f(z)-f(z)$ is the amplitude and frequency sum $\sigma H_{\nu}(\{\alpha_k\},\{r
\beta_k\},h;z)$. We emphasize that the above-mentioned variation of $s_m=s_{m}(h,f)$ in the framework of the interpolation problem is universal as it depends only on $\max \{|s_m|\}$ but not on the functional properties of $f$ and $h$. Moreover, as we will see below, if $\alpha_k$, $\beta_k$, $\sigma$, $r$ are chosen appropriately, then the difference $\tilde f-f$ is just a certain binomial. Let us describe the regularization method in detail. Instead of the function $f$, whose corresponding problem (\[SRS\]) is not regular, we introduce the varied function $$\label{F(z)} {\tilde f}(z):=f(z)+\sigma H_{\nu}(\{\alpha_k\},\{r
\beta_k\},h;z),\qquad p\in \mathbb{C},\qquad {\nu}\in \mathbb{N},$$ where $\alpha_k$, $\beta_k$ $\sigma$, $r$ are constants. Since $${\tilde f}(z)= \sum_{m=0}^\infty f_m z^m
+\sigma\sum_{k=1}^{\nu}\alpha_k \sum_{m=0}^\infty h_m (r
\beta_kz)^m= \sum_{m=0}^\infty \left(s_m+\tau_m \right)h_m z^m,$$ where $\tau_m:=\sigma\sum_{k=1}^{\nu}\alpha_k (r\beta_k)^m$ and $s_m=s_{m}(h,f)$ as above (see (\[ssmm\])), instead of $(\ref{SRS})$ we obtain the system $$\label{Var_disc_mom_syst} \sum_{k=1}^n \mu_k
\lambda_k^m=s_m+\tau_m, \qquad m=\overline{0,2n-1},$$ which differs from the system (\[SRS\]) in 