@article{Teteruk_2020, title={Two-dimensional generalized instantaneous images and approximations of the Pade type function of two variables}, url={https://bphm.knu.ua/index.php/bphm/article/view/174}, DOI={10.17721/1812-5409.2020/1-2.13}, abstractNote={<p>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.</p><p><em><strong><span lang="EN-US">Key words</span></strong></em><span lang="EN-US">: Pade approximation, instantaneous image, hypergeometric series, rational approximation.</span></p><p><em><strong><span lang="EN-US">Pages of the article in the issue</span></strong></em><span lang="EN-US">: 75 - 80</span></p><p><strong><em><span lang="EN-US">Language of the article</span></em></strong><span lang="EN-US">: Ukrainian</span></p>}, number={1-2}, journal={Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences}, author={Teteruk, I. S.}, year={2020}, month={Mar.}, pages={75–80} }