Two-dimensional generalized instantaneous images and approximations of the Pade type function of two variables, which is a generalization of hypergeometric series

Тип публікації :
Стаття
Дата випуску :
2021
Автор(и) :
Тетерук, І. С.
Мова основного тексту :
Англійська
eKNUTSHIR URL :
DOI :
Журнал :
Випуск :
2
ISSN :
1812-5409
Початкова сторінка :
95
Кінцева сторінка :
100
Цитування :
[APA 7] Тетерук, І. С. (2021). Two-dimensional generalized instantaneous images and approximations of the Pade type function of two variables, which is a generalization of hypergeometric series. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics, (2), 95–100. https://doi.org/10.17721/1812-5409.2021/2.13
[ДСТУ] Тетерук І. С. Two-dimensional generalized instantaneous images and approximations of the Pade type function of two variables, which is a generalization of hypergeometric series. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics. 2021. no. 2. P. 95—100. DOI: 10.17721/1812-5409.2021/2.13 (date of access: 25.07.2026).
Generalized instantaneous image were introduced by V.K. Dzyaduk in 1981 and proved to be aconvenient tool for constructing and studying the Padé approximants and their generalizations. The method of generalized instantaneous images proposed by Dzyadyk madeit possible to construct and studyrational 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, namely with the q-analog of the exponent e_q.
Pages of the article in the issue: 95 - 100
Language of the article: Ukrainian
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