can deduce it from [@Abramovitz §25.4.38] by a suitable change of variables.

[**.3. Padé approximants.**]{} The Padé approximants as well as the Gaussian quadratures are closely related to the classical moment problem (see, for instance, [@Dzyadyk]). Construction of the amplitude and frequency sum $H_n(\{\mu_k\},\{\lambda_k\},h;x)$ with the basis function $h(z)=(z-1)^{-1}$ for some function $f$, analytic in a neighbourhood of the origin, leads to the sequence of moments $s_m=-f_m$, $m=\overline{0,2n-1}$. If the generating polynomial (\[G\_n\]) for this sequence is of degree $n$ and all its roots are pairwise distinct, then by Theorem \[th1\] we get the following interpolation identity: $$\label{2}
f(z)=\sum_{k=1}^n\frac{\mu_k}{\lambda_kz-1}+O(z^{2n}).$$ This is a classical Padé approximant of order $[(n-1)/n]$. We recall that classical Padé approximants of order $[m/n]$ are interpolating rational functions of the form $P_m(f;z)/Q_n(f;z)$ (see, for instance, [@Baker §1.1]). Note that the method for solving the problem (\[SRS\]), proposed by Ramanujan [@Ramanujan], is equivalent to the one for construction of the interpolation formula (\[2\]) (see [@Lyubich; @Lyubich2]).

[**.4. Exponential sums.**]{} Let $h(z)=\exp(z)$ be a basis function in the amplitude and frequency operator $H_n(\{\mu_k\},\{\lambda_k\},h;z)$ and $f$ be a function, which we are going to interpolate. The corresponding sequence of moments is $s_m=m!f_m$, $m=\overline{0,2n-1}$. Suppose that the problem (\[SRS\]) for this 