the formula (\[f\_reg\_expansion\]) and Theorem \[th1\] we obtain the following result.

\[th2\] Given $p$ and $q$ sufficiently large in modulus, the varied problem $(\ref{Var_disc_mom_syst})$ with the parameters $(\ref{TAU})$ has a regular solution $\{\mu_k\}$, $\{\lambda_k\}$. Moreover, for the constants $c_1=-ph_{n-1}$ and $c_2=-qh_{2n-1}$ the following interpolation formula holds: $$f(z)=c_1z^{n-1}+c_2 z^{2n-1}+\sum_{k=1}^n\mu_k h(\lambda_k
z)+O(z^{2n}).$$

\[REG+++\] The above-mentioned regularization with the parameters from (\[alpha-beta\]) and (\[TAU\]) is actually equivalent to adding the binomial $c_1z^{n-1}+c_2 z^{2n-1}$ with non-vanishing coefficients $c_{1}$ and $c_{2}$ to the function $f$. In what follows we will expand the class of regularizable problems by showing that $c_1$ and $c_2$ can be chosen in a different way and not necessarily non-vanishing. In particular, in the extrapolation problem from Section \[par-extrap\] it will be reasonable to set $c_2=0$.

\[rem2\] The conditions on $p$ and $q$, mentioned in Theorem \[th2\], are quite qualitative and need additional specification in practice. Several methods for this will be proposed below in particular applications. In the general case one can use the following observations. The leading coefficient $g_n=g_n(p)$ of the polynomial ${G}_n$ is obviously a polynomial of $p$ of degree $n$, hence $\deg
{G}_n(p,q;\lambda)=n$ for all $p$ except those from the set $$\label{Pi-general} \Pi:=\{p: g_n(p)=0\},$$ containing no more than 