On Analytical Continuation of the Horn’s Hypergeometric Functions <i>H</i><sub>3</sub> and Their Ratios
This paper considers the Horn’s hypergeometric function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mn>3</mn></msub></semantics></math></inline-f...
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MDPI AG
2025-01-01
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| 丛编: | Axioms |
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| 在线阅读: | https://www.mdpi.com/2075-1680/14/1/67 |
| _version_ | 1826858283609096192 |
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| author | Roman Dmytryshyn Tamara Antonova Sofiia Hladun |
| author_facet | Roman Dmytryshyn Tamara Antonova Sofiia Hladun |
| author_sort | Roman Dmytryshyn |
| collection | DOAJ |
| description | This paper considers the Horn’s hypergeometric function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mn>3</mn></msub></semantics></math></inline-formula>, which is closely related to other hypergeometric functions and has various mathematical or physical applications. The problem of analytical extension of this function is solved using a special family of functions—branched continued fractions. A new domain of analytical extension of the Horn’s hypergeometric functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mn>3</mn></msub></semantics></math></inline-formula> and their ratios under certain conditions to real parameters are established. This paper also contains an example of the presentation and continuation of some special function and an analysis of numerical results. |
| first_indexed | 2025-02-16T18:55:58Z |
| format | Article |
| id | doaj.art-aa44301aad5c46bb9f02c8d6bc9769d5 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2025-02-16T18:55:58Z |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-aa44301aad5c46bb9f02c8d6bc9769d52025-01-24T13:22:19ZengMDPI AGAxioms2075-16802025-01-011416710.3390/axioms14010067On Analytical Continuation of the Horn’s Hypergeometric Functions <i>H</i><sub>3</sub> and Their RatiosRoman Dmytryshyn0Tamara Antonova1Sofiia Hladun2Faculty of Mathematics and Computer Science, Vasyl Stefanyk Precarpathian National University, 57 Shevchenko Str., 76018 Ivano-Frankivsk, UkraineInstitute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, 12 Stepan Bandera Str., 79013 Lviv, UkraineInstitute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, 12 Stepan Bandera Str., 79013 Lviv, UkraineThis paper considers the Horn’s hypergeometric function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mn>3</mn></msub></semantics></math></inline-formula>, which is closely related to other hypergeometric functions and has various mathematical or physical applications. The problem of analytical extension of this function is solved using a special family of functions—branched continued fractions. A new domain of analytical extension of the Horn’s hypergeometric functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mn>3</mn></msub></semantics></math></inline-formula> and their ratios under certain conditions to real parameters are established. This paper also contains an example of the presentation and continuation of some special function and an analysis of numerical results.https://www.mdpi.com/2075-1680/14/1/67hypergeometric functionbranched continued fractionanalytical continuationconvergenceapproximation by rational functions |
| spellingShingle | Roman Dmytryshyn Tamara Antonova Sofiia Hladun On Analytical Continuation of the Horn’s Hypergeometric Functions <i>H</i><sub>3</sub> and Their Ratios Axioms hypergeometric function branched continued fraction analytical continuation convergence approximation by rational functions |
| title | On Analytical Continuation of the Horn’s Hypergeometric Functions <i>H</i><sub>3</sub> and Their Ratios |
| title_full | On Analytical Continuation of the Horn’s Hypergeometric Functions <i>H</i><sub>3</sub> and Their Ratios |
| title_fullStr | On Analytical Continuation of the Horn’s Hypergeometric Functions <i>H</i><sub>3</sub> and Their Ratios |
| title_full_unstemmed | On Analytical Continuation of the Horn’s Hypergeometric Functions <i>H</i><sub>3</sub> and Their Ratios |
| title_short | On Analytical Continuation of the Horn’s Hypergeometric Functions <i>H</i><sub>3</sub> and Their Ratios |
| title_sort | on analytical continuation of the horn s hypergeometric functions i h i sub 3 sub and their ratios |
| topic | hypergeometric function branched continued fraction analytical continuation convergence approximation by rational functions |
| url | https://www.mdpi.com/2075-1680/14/1/67 |
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