The two-dimensional g-fraction with independent variables for double power series

In this paper the two-dimensional g-fraction with independent variables which is the generalization of the continued g-fraction is considered. The correspondence between the formal double power series and the above mentioned fraction is studied. As a result the algorithm for the expansion of the for...

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Bibliographic Details
Published in:Journal of approximation theory 2012-12, Vol.164 (12), p.1520-1539
Main Author: Dmytryshyn, R.I.
Format: Article
Language:English
Subjects:
Convergence
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Two-dimensional [formula omitted]-fraction with independent variables
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Summary:In this paper the two-dimensional g-fraction with independent variables which is the generalization of the continued g-fraction is considered. The correspondence between the formal double power series and the above mentioned fraction is studied. As a result the algorithm for the expansion of the formal double power series into the corresponding two-dimensional g-fraction with independent variables has been constructed and the conditions for the existence of such an algorithm have been established. The expansion of some functions into the corresponding two-dimensional g-fraction with independent variables is constructed and the efficiency of the obtained expansion by using approximants is shown.
ISSN:0021-9045
1096-0430
DOI:10.1016/j.jat.2012.09.002