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

• Date: 2010
• Main Authors: Buslaev, V. I., Буслаев, В. И.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2010
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2870
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 v...