Two-dimensional generalized instantaneous images and approximations of the Pade type function of two variables, which is a generalization of hypergeometric series
DOI:
https://doi.org/10.17721/1812-5409.2021/2.13Keywords:
Pade approximation, instantaneous image, hypergeometric series, rational approximationAbstract
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
References
DZYADYK V. K., (1981) On the generalization of the problem of moments, Dop. AN URSR 6, p. 8–12. (In Ukrainian)
GOLUB A. P., (2002) Generalized moment representations and Pade approximants, Proceedings of the Institute of Mathematics NAS Ukraine, 222 p. (In Ukrainian)
BEJKER DZH. and GREJVS-MORRIS P.R., Padé Approximants (1986), 502 p.
GOLUB A. P. and CHERNECKA L. O., (2013) Two Dimensional Generalized Moment Representations and Rational Approximations of Functions of Two Variables, UMJ 65,8, p. 1035–1058. (In Ukrainian)
GOLUB A. P., (1981) Generalized moment representations of basic hypergeometric series, UMJ 41 №6, p. 803-808. (In Russian)
GOLUB A. P., (1989) On one kind of generalized moment representations, UMJ 41 №11 (1989), p.1455-1460. (In Russian)
GOLUB A. P., (2015) Padé approximants of q-analogues, exponents and their generalizations, Theory of approximation of functions and related questions. Proceedings of the Institute of Mathematics NAS Ukraine T.12 №4, p. 144–153. (In Ukrainian)
GOLUB A. P. and TETERUK I. S., (2019) Generalized instantaneous images and Pade-type approximants of some basic hypergeometric series of two variables, Proceedings of the Institute of Mathematics NAS Ukraine t.16 №2, p. 16–23 (In Ukrainian)
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
