Truncation error bounds for branched continued fraction $\sum_{i_1=1}^N\frac{a_{i(1)}}{1}{\atop+}\sum_{i_2=1}^{i_1}\frac{a_{i(2)}}{1}{\atop+}\sum_{i_3=1}^{i_2}\frac{a_{i(3)}}{1}{\atop+}\ldots$
UDC 517.5 The paper deals with the problem of estimating the error of approximation of a branched continued fraction, which is a generalization of a continued fraction. Using the method of fundamental inequalities, truncation error bounds for branched continued fraction $\sum_{i_1=1}^N\frac{a_{i(1)}...
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| Date: | 2020 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2020
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/2342 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.5
The paper deals with the problem of estimating the error of approximation of a branched continued fraction, which is a generalization of a continued fraction. Using the method of fundamental inequalities, truncation error bounds for branched continued fraction $\sum_{i_1=1}^N\frac{a_{i(1)}}{1}{\atop+}\sum_{i_2=1}^{i_1}\frac{a_{i(2)}}{1}{\atop+}\sum_{i_3=1}^{i_2}\frac{a_{i(3)}}{1}{\atop+}\ldots,$ whose elements belong to some rectangular sets of a complex plane, are established. The obtained results have been applied to multidimensional $S$, $A$-fraction with independent variables. |
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| DOI: | 10.37863/umzh.v72i7.2342 |