On the domains of convergence of the branched continued fraction expansion of ratio $H_4(a,d+1;c,d;\mathbf{z})/H_4(a,d+2;c,d+1;\mathbf{z})$
The paper considers the problem of establishing the convergence criteria of the branched continued fraction expansion of the ratio of Horn's hypergeometric functions $H_4$. To solve it, the technique of expanding the domain of convergence of the branched continued fraction from the known small...
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| Format: | Article |
| Language: | English |
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Oles Honchar Dnipro National University
2023-12-01
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| Series: | Researches in Mathematics |
| Subjects: | |
| Online Access: | https://vestnmath.dnu.dp.ua/index.php/rim/article/view/406/406 |
| _version_ | 1797375338674651136 |
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| author | R.I. Dmytryshyn I.-A.V. Lutsiv O.S. Bodnar |
| author_facet | R.I. Dmytryshyn I.-A.V. Lutsiv O.S. Bodnar |
| author_sort | R.I. Dmytryshyn |
| collection | DOAJ |
| description | The paper considers the problem of establishing the convergence criteria of the branched continued fraction expansion of the ratio of Horn's hypergeometric functions $H_4$. To solve it, the technique of expanding the domain of convergence of the branched continued fraction from the known small domain of convergence to a wider domain of convergence is used. For the real and complex parameters of the Horn hypergeometric function $H_4$, a number of convergence criteria of the branched continued fraction expansion under certain conditions to its coefficients in various unbounded domains of the space have been established. |
| first_indexed | 2024-03-08T19:22:50Z |
| format | Article |
| id | doaj.art-bf63289a055941cda7cae26cab281692 |
| institution | Directory Open Access Journal |
| issn | 2664-4991 2664-5009 |
| language | English |
| last_indexed | 2024-03-08T19:22:50Z |
| publishDate | 2023-12-01 |
| publisher | Oles Honchar Dnipro National University |
| record_format | Article |
| series | Researches in Mathematics |
| spelling | doaj.art-bf63289a055941cda7cae26cab2816922023-12-26T17:23:11ZengOles Honchar Dnipro National UniversityResearches in Mathematics2664-49912664-50092023-12-01312192510.15421/242311On the domains of convergence of the branched continued fraction expansion of ratio $H_4(a,d+1;c,d;\mathbf{z})/H_4(a,d+2;c,d+1;\mathbf{z})$R.I. Dmytryshyn0https://orcid.org/0000-0003-2845-0137I.-A.V. Lutsiv1https://orcid.org/0000-0002-4100-2972O.S. Bodnar2https://orcid.org/0000-0003-4207-0624Vasyl Stefanyk Precarpathian National UniversityVasyl Stefanyk Precarpathian National UniversityTernopil Volodymyr Hnatiuk National Pedagogical UniversityThe paper considers the problem of establishing the convergence criteria of the branched continued fraction expansion of the ratio of Horn's hypergeometric functions $H_4$. To solve it, the technique of expanding the domain of convergence of the branched continued fraction from the known small domain of convergence to a wider domain of convergence is used. For the real and complex parameters of the Horn hypergeometric function $H_4$, a number of convergence criteria of the branched continued fraction expansion under certain conditions to its coefficients in various unbounded domains of the space have been established.https://vestnmath.dnu.dp.ua/index.php/rim/article/view/406/406horn hypergeometric functionbranched continued fractionholomorphic function of several complex variablesconvergence |
| spellingShingle | R.I. Dmytryshyn I.-A.V. Lutsiv O.S. Bodnar On the domains of convergence of the branched continued fraction expansion of ratio $H_4(a,d+1;c,d;\mathbf{z})/H_4(a,d+2;c,d+1;\mathbf{z})$ Researches in Mathematics horn hypergeometric function branched continued fraction holomorphic function of several complex variables convergence |
| title | On the domains of convergence of the branched continued fraction expansion of ratio $H_4(a,d+1;c,d;\mathbf{z})/H_4(a,d+2;c,d+1;\mathbf{z})$ |
| title_full | On the domains of convergence of the branched continued fraction expansion of ratio $H_4(a,d+1;c,d;\mathbf{z})/H_4(a,d+2;c,d+1;\mathbf{z})$ |
| title_fullStr | On the domains of convergence of the branched continued fraction expansion of ratio $H_4(a,d+1;c,d;\mathbf{z})/H_4(a,d+2;c,d+1;\mathbf{z})$ |
| title_full_unstemmed | On the domains of convergence of the branched continued fraction expansion of ratio $H_4(a,d+1;c,d;\mathbf{z})/H_4(a,d+2;c,d+1;\mathbf{z})$ |
| title_short | On the domains of convergence of the branched continued fraction expansion of ratio $H_4(a,d+1;c,d;\mathbf{z})/H_4(a,d+2;c,d+1;\mathbf{z})$ |
| title_sort | on the domains of convergence of the branched continued fraction expansion of ratio h 4 a d 1 c d mathbf z h 4 a d 2 c d 1 mathbf z |
| topic | horn hypergeometric function branched continued fraction holomorphic function of several complex variables convergence |
| url | https://vestnmath.dnu.dp.ua/index.php/rim/article/view/406/406 |
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