On branched continued fraction expansions of hypergeometric functions \(F_M\) and their ratios
The paper investigates the problem of constructing branched continued fraction expansions of hypergeometric functions \(F_M(a_1,a_2,b_1,b_2;a_1,c_2;\mathbf{z})\) and their ratios. Recurrence relations of the hypergeometric function \(F_M\) are established, which provide the construction of formal br...
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| Format: | Article |
| Language: | English |
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Tuncer Acar
2025-03-01
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| Series: | Modern Mathematical Methods |
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| Online Access: | https://modernmathmeth.com/index.php/pub/article/view/52 |
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| author | Ivan Nyzhnyk Roman Dmytryshyn Tamara Antonova |
| author_facet | Ivan Nyzhnyk Roman Dmytryshyn Tamara Antonova |
| author_sort | Ivan Nyzhnyk |
| collection | DOAJ |
| description | The paper investigates the problem of constructing branched continued fraction expansions of hypergeometric functions \(F_M(a_1,a_2,b_1,b_2;a_1,c_2;\mathbf{z})\) and their ratios. Recurrence relations of the hypergeometric function \(F_M\) are established, which provide the construction of formal branched continued fractions with simple structures, the elements of which are polynomials in the variables \(z_1, z_2, z_3.\) To construct the expansions, a method of based on the so-called complete group of ratios of hypergeometric functions was used, which is a generalization of the classical Gauss method. |
| format | Article |
| id | doaj-art-64a5c32f77de42f7b2b58137496ffeec |
| institution | DOAJ |
| issn | 3023-5294 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Tuncer Acar |
| record_format | Article |
| series | Modern Mathematical Methods |
| spelling | doaj-art-64a5c32f77de42f7b2b58137496ffeec2025-08-20T03:03:40ZengTuncer AcarModern Mathematical Methods3023-52942025-03-013152On branched continued fraction expansions of hypergeometric functions \(F_M\) and their ratiosIvan Nyzhnyk0https://orcid.org/0009-0009-8434-687XRoman Dmytryshyn1https://orcid.org/0000-0003-2845-0137Tamara Antonova2https://orcid.org/0000-0002-0358-4641Vasyl Stefanyk Precarpathian National UniversityVasyl Stefanyk Precarpathian National UniversityLviv Polytechnic National UniversityThe paper investigates the problem of constructing branched continued fraction expansions of hypergeometric functions \(F_M(a_1,a_2,b_1,b_2;a_1,c_2;\mathbf{z})\) and their ratios. Recurrence relations of the hypergeometric function \(F_M\) are established, which provide the construction of formal branched continued fractions with simple structures, the elements of which are polynomials in the variables \(z_1, z_2, z_3.\) To construct the expansions, a method of based on the so-called complete group of ratios of hypergeometric functions was used, which is a generalization of the classical Gauss method.https://modernmathmeth.com/index.php/pub/article/view/52hypergeometric functionrecurrence relationbranched continued fractionapproximation by rational functions |
| spellingShingle | Ivan Nyzhnyk Roman Dmytryshyn Tamara Antonova On branched continued fraction expansions of hypergeometric functions \(F_M\) and their ratios Modern Mathematical Methods hypergeometric function recurrence relation branched continued fraction approximation by rational functions |
| title | On branched continued fraction expansions of hypergeometric functions \(F_M\) and their ratios |
| title_full | On branched continued fraction expansions of hypergeometric functions \(F_M\) and their ratios |
| title_fullStr | On branched continued fraction expansions of hypergeometric functions \(F_M\) and their ratios |
| title_full_unstemmed | On branched continued fraction expansions of hypergeometric functions \(F_M\) and their ratios |
| title_short | On branched continued fraction expansions of hypergeometric functions \(F_M\) and their ratios |
| title_sort | on branched continued fraction expansions of hypergeometric functions f m and their ratios |
| topic | hypergeometric function recurrence relation branched continued fraction approximation by rational functions |
| url | https://modernmathmeth.com/index.php/pub/article/view/52 |
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