Тип публикации: статья из журнала
Год издания: 2018
Идентификатор DOI: 10.1134/S1064562418010131
Аннотация: The Puiseux series generated by the power function z = w (1/rho), where rho > 0,rho not equal 1, is considered. A version of the Plya-Bernstein theorem for an entire function of order rho not equal 1 and normal type is proposed and applied to describe the domain of analytic continuation of this series. The domain of summability of Показать полностьюa "regular" Puiseux series is found (this is a many-sheeted "Borel polygon"); in the case rho = 1, the "one-sheeted" result of Borel is substantially extended. These results make it possible to describe domains of analytic continuation of the Puiseux expansions of popular many-sheeted functions (such as inverses of rational functions).
Журнал: DOKLADY MATHEMATICS
Выпуск журнала: Vol. 97, Is. 1
Номера страниц: 42-46
ISSN журнала: 10645624
Место издания: NEW YORK
Издатель: MAIK NAUKA/INTERPERIODICA/SPRINGER