We obtain explicit formulas that express the Hankel determinants of functions given by their expansions in continued P-fractions in terms of the parameters of the fraction. As a corollary, we obtain a lower bound for the capacity of the set of singular points of these functions, an analog of the van Vleck theorem for P-fractions with limit-periodic coefficients, another proof of the Gonchar theorem on the Leighton conjecture, and an upper bound for the radius of the disk of meromorphy of a function given by a C-fraction.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 3, pp. 315–326, March, 2010.
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Buslaev, V.I. On Hankel determinants of functions given by their expansions in P-fractions. Ukr Math J 62, 358–372 (2010). https://doi.org/10.1007/s11253-010-0359-x
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DOI: https://doi.org/10.1007/s11253-010-0359-x