On Senatov moments in asymptotic expansions in the central limit theorem

Representations are put forward for the moments and the truncated Senatov quasi-moments of normalized sums of random variables (r.v.'s) in terms of the Senatov moments of the original distribution. These representations make possible the direct transition from new asymptotic expansions in the central limit theorem to Gram–Charlier type expansions and are applied in the new proof of formulas for the convergence rate of these moments.