دورية أكاديمية
On the convergence of multidimensional S-fractions with independent variables
| العنوان: | On the convergence of multidimensional S-fractions with independent variables |
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| المؤلفون: | O.S. Bodnar, R.I. Dmytryshyn, S.V. Sharyn |
| المصدر: | Karpatsʹkì Matematičnì Publìkacìï, Vol 12, Iss 2, Pp 353-359 (2020) |
| بيانات النشر: | Vasyl Stefanyk Precarpathian National University, 2020. |
| سنة النشر: | 2020 |
| المجموعة: | LCC:Mathematics |
| مصطلحات موضوعية: | branched continued fraction, convergence criterion, uniform convergence, estimates of the rate of convergence, continued fraction, Mathematics, QA1-939 |
| الوصف: | The paper investigates the convergence problem of a special class of branched continued fractions, i.e. the multidimensional S-fractions with independent variables, consisting of \[\sum_{i_1=1}^N\frac{c_{i(1)}z_{i_1}}{1}{\atop+}\sum_{i_2=1}^{i_1}\frac{c_{i(2)}z_{i_2}}{1}{\atop+} \sum_{i_3=1}^{i_2}\frac{c_{i(3)}z_{i_3}}{1}{\atop+}\cdots,\] which are multidimensional generalizations of S-fractions (Stieltjes fractions). These branched continued fractions are used, in particular, for approximation of the analytic functions of several variables given by multiple power series. For multidimensional S-fractions with independent variables we have established a convergence criterion in the domain \[H=\left\{{\bf{z}}=(z_1,z_2,\ldots,z_N)\in\mathbb{C}^N:\;|\arg(z_k+1)| |
| نوع الوثيقة: | article |
| وصف الملف: | electronic resource |
| اللغة: | English Ukrainian |
| تدمد: | 2075-9827 2313-0210 |
| Relation: | https://journals.pnu.edu.ua/index.php/cmp/article/view/4320; https://doaj.org/toc/2075-9827; https://doaj.org/toc/2313-0210 |
| DOI: | 10.15330/cmp.12.2.353-359 |
| URL الوصول: | https://doaj.org/article/2150c25458ef4d0da23dd020c80b756a |
| رقم الأكسشن: | edsdoj.2150c25458ef4d0da23dd020c80b756a |
| قاعدة البيانات: | Directory of Open Access Journals |
Full Text Finder | تدمد: | 20759827 23130210 |
|---|---|
| DOI: | 10.15330/cmp.12.2.353-359 |