Open Access10.17721/1812-5409.2021/2
Author(s) -
I. S. Teteruk,
AUTHOR_ID
Publication year - 2021
Publication title -
vìsnik. serìâ fìziko-matematičnì nauki/vìsnik kiì̈vsʹkogo nacìonalʹnogo unìversitetu ìmenì tarasa ševčenka. serìâ fìziko-matematičnì nauki
Language(s) - English
Resource type - Journals
eISSN - 2218-2055
pISSN - 1812-5409
DOI - 10.17721/1812-5409.2021/2.13
Subject(s) - padé approximant , hypergeometric function , mathematics , sequence (biology) , generalized hypergeometric function , function (biology) , series (stratigraphy) , pure mathematics , exponent , exponential function , rational function , image (mathematics) , class (philosophy) , mathematical analysis , computer science , paleontology , linguistics , philosophy , genetics , evolutionary biology , artificial intelligence , biology
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.