Two-dimensional generalized instantaneous images and approximations of the Pade type function of two variables

Teteruk, I. S. (2020). Two-dimensional generalized instantaneous images and approximations of the Pade type function of two variables. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics(1), 75–80. https://doi.org/10.17721/1812-5409.2020/1-2.13

Generalized instantaneous image were introduced by V.K. Dzyaduk [1] in 1981 and proved to be a convenient tool for constructing and studying the Padé approximants and their generalizations (see [2]). The method of generalized instantaneous images proposed by Dzyadyk made it possible to construct and study rational Padé approximants and their generalizations for many classes of special functions from a single position. As an example, the Padé approximants is constructed for a class of basic hypergeometric series, which includes a q-analogue of the exponential function. In this paper the construction of the Pade approximants for the function of two variables is investigated. A two-dimensional functional sequence is constructed, which has a generalized instantaneous image, and rational approximants are determined, which will be generalizations of one-dimensional Padé approximants. The function of the two variables is entirely related to the basic hypergeometric series.Key words: Pade approximation, instantaneous image, hypergeometric series, rational approximation.Pages of the article in the issue: 75 - 80Language of the article: Ukrainian