On the branched continued fraction expansions of the complete group of ratios of the generalized hypergeometric function $_4F_3$
The paper considers the classical problem of the rational approximation of analytic functions of complex variable, in particulary, to issues that arise when constructing branched continued fraction expansions for generalized hypergeometric functions. Using combinations of three- and four-term recurr...
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| Format: | Article |
| Language: | English |
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Oles Honchar Dnipro National University
2024-12-01
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| Series: | Researches in Mathematics |
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| Online Access: | https://vestnmath.dnu.dp.ua/index.php/rim/article/view/436/436 |
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| author | Y. Lutsiv T. Antonova R. Dmytryshyn M. Dmytryshyn |
| author_facet | Y. Lutsiv T. Antonova R. Dmytryshyn M. Dmytryshyn |
| author_sort | Y. Lutsiv |
| collection | DOAJ |
| description | The paper considers the classical problem of the rational approximation of analytic functions of complex variable, in particulary, to issues that arise when constructing branched continued fraction expansions for generalized hypergeometric functions. Using combinations of three- and four-term recurrence relations of the generalized hypergeometric function $_4F_3$, we constructed the formal branched continued fraction expansions of sixteen ratios of this function. These sixteen ratios are the complete group of ratios of the generalized hypergeometric function $_4F_3$. This means that each of these ratios has a formal branched continued fraction expansion that uses all of these ratios. |
| format | Article |
| id | doaj-art-f67b2afb458f4bc798e68b7d242c4486 |
| institution | Kabale University |
| issn | 2664-4991 2664-5009 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Oles Honchar Dnipro National University |
| record_format | Article |
| series | Researches in Mathematics |
| spelling | doaj-art-f67b2afb458f4bc798e68b7d242c44862025-01-05T19:37:20ZengOles Honchar Dnipro National UniversityResearches in Mathematics2664-49912664-50092024-12-0132211513210.15421/242423On the branched continued fraction expansions of the complete group of ratios of the generalized hypergeometric function $_4F_3$Y. Lutsiv0T. Antonova1https://orcid.org/0000-0002-0358-4641R. Dmytryshyn2https://orcid.org/0000-0003-2845-0137M. Dmytryshyn3https://orcid.org/0000-0002-0609-9764Vasyl Stefanyk Precarpathian National UniversityLviv Polytechnic National UniversityVasyl Stefanyk Precarpathian National UniversityWest Ukrainian National UniversityThe paper considers the classical problem of the rational approximation of analytic functions of complex variable, in particulary, to issues that arise when constructing branched continued fraction expansions for generalized hypergeometric functions. Using combinations of three- and four-term recurrence relations of the generalized hypergeometric function $_4F_3$, we constructed the formal branched continued fraction expansions of sixteen ratios of this function. These sixteen ratios are the complete group of ratios of the generalized hypergeometric function $_4F_3$. This means that each of these ratios has a formal branched continued fraction expansion that uses all of these ratios.https://vestnmath.dnu.dp.ua/index.php/rim/article/view/436/436hypergeometric functionbranched continued fractionapproximation by rational functions |
| spellingShingle | Y. Lutsiv T. Antonova R. Dmytryshyn M. Dmytryshyn On the branched continued fraction expansions of the complete group of ratios of the generalized hypergeometric function $_4F_3$ Researches in Mathematics hypergeometric function branched continued fraction approximation by rational functions |
| title | On the branched continued fraction expansions of the complete group of ratios of the generalized hypergeometric function $_4F_3$ |
| title_full | On the branched continued fraction expansions of the complete group of ratios of the generalized hypergeometric function $_4F_3$ |
| title_fullStr | On the branched continued fraction expansions of the complete group of ratios of the generalized hypergeometric function $_4F_3$ |
| title_full_unstemmed | On the branched continued fraction expansions of the complete group of ratios of the generalized hypergeometric function $_4F_3$ |
| title_short | On the branched continued fraction expansions of the complete group of ratios of the generalized hypergeometric function $_4F_3$ |
| title_sort | on the branched continued fraction expansions of the complete group of ratios of the generalized hypergeometric function 4f 3 |
| topic | hypergeometric function branched continued fraction approximation by rational functions |
| url | https://vestnmath.dnu.dp.ua/index.php/rim/article/view/436/436 |
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