2018
Том 70
№ 2

# On Hankel determinants of functions given by their expansions in $P$-fractions

Buslaev V. I.

Abstract

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 $С$-fraction.

English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 3, pp 358-372.

Citation Example: Buslaev V. I. On Hankel determinants of functions given by their expansions in $P$-fractions // Ukr. Mat. Zh. - 2010. - 62, № 3. - pp. 315–326.

Full text