In this paper a convergence class is characterized for special series associated with Gelfond's interpolation problem (a generalization of the Abel-Goncharov problem) when the interpolation nodes are equidistantly distributed within the interval $[0,1]$. As a result, an expansion is derived of the arithmetic-geometric mean difference in terms of certain central moments. Another result concerns an expansion of the Hellinger integral.

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CWI. Probability, Networks and Algorithms [PNA]
Stochastics

Dzhaparidze, K.O. (1998). On interpolation series related to the Abel-Goncharov problem, with applications to arithmetic-geometric mean relationship and Hellinger integrals. CWI. Probability, Networks and Algorithms [PNA]. CWI.