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

Teteruk, I. S.

doi:10.17721/1812-5409.2020/1-2.13

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

Тип публікації :

Стаття

Дата випуску :

2020

Автор(и) :

Teteruk, I. S.

Мова основного тексту :

Англійська

eKNUTSHIR URL :

https://ir.library.knu.ua/handle/15071834/26153

DOI :

10.17721/1812-5409.2020/1-2.13

Журнал :

Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics

Випуск :

1

ISSN :

1812-5409

Початкова сторінка :

75

Кінцева сторінка :

80

Цитування :

[APA 7] 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

[ДСТУ] Teteruk I. S. 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. 2020. no. 1. P. 75—80. DOI: 10.17721/1812-5409.2020/1-2.13 (date of access: 25.07.2026).

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

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