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

  • I. S. Teteruk Institute of Mathematics of NASU, Kyiv

Abstract

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 - 80

Language of the article: Ukrainian

References

Dzyadik V. K., Pro uzagalnennya problemi momentiv, Dop.AN URSR 6 (1981), 8–12.

Golub A. P., Uzagalneni momentni zobrazhennya ta aproksimaciyi Pade, Kiyiv: In-t matematiki NAN Ukrayini, (2002), 222.

Bejker Dzh. and Grejvs-Morris P.R., Aproksimacii Pade (1986), 502.

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Golub A. P., Obobshennye momentnye predstavleniya bazisnyh gipergeometricheskih ryadov, Ukr.mat.zhurn. 41 №6 (1981), 803-808.

Golub A. P., Ob odnoj raznovidnosti obobshennyh momentnyh predstavlenij, Ukr.mat.zhurn. 41 №11 (1989), 1455-1460.

Golub A. P., Aproksimanti Pade q-analogiv eksponenti ta yih uzagalnen, Teoriya nablizhennya funkcij ta sumizhni pitannya. Zbirnik prac Institutu matematiki NAN Ukrayini T.12 №4 (2015), 144–153.

Golub A. P. and Teteruk I. S., Uzagalneni momentni zobrazhennya ta aproksimanti tipu Pade deyakih bazisnih gipergeometrichnih ryadiv dvoh zminnih, Zbirnik prac Institutu matematiki NAN Ukrayini t.16 №2 (2019), 1–8.

How to Cite
Teteruk, I. S. (1). Two-dimensional generalized instantaneous images and approximations of the Pade type function of two variables. Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, (1-2), 75-80. https://doi.org/10.17721/1812-5409.2020/1-2.13
Section
Differential equations, mathematical physics and mechanics