On Analytical Extension of Generalized Hypergeometric Function <sub>3</sub><i>F</i><sub>2</sub>
The paper considers the generalized hypergeometric function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mmultiscripts><mi>F</mi><mn>2</mn><none></none><mpr...
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MDPI AG
2024-10-01
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| Online Access: | https://www.mdpi.com/2075-1680/13/11/759 |
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| author | Roman Dmytryshyn Volodymyra Oleksyn |
| author_facet | Roman Dmytryshyn Volodymyra Oleksyn |
| author_sort | Roman Dmytryshyn |
| collection | DOAJ |
| description | The paper considers the generalized hypergeometric function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mmultiscripts><mi>F</mi><mn>2</mn><none></none><mprescripts></mprescripts><mn>3</mn><none></none></mmultiscripts><mo>,</mo></mrow></semantics></math></inline-formula> which is important in various fields of mathematics, physics, and economics. The method is used, according to which the domains of the analytical continuation of the special functions are the domains of convergence of their expansions into a special family of functions, namely branched continued fractions. These expansions have wide domains of convergence and better computational properties, particularly compared with series, making them effective tools for representing special functions. New domains of the analytical continuation of the generalized hypergeometric function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mmultiscripts><mi>F</mi><mn>2</mn><none></none><mprescripts></mprescripts><mn>3</mn><none></none></mmultiscripts></mrow></semantics></math></inline-formula> with real and complex parameters have been established. The paper also includes examples of the presentation and extension of some special functions. |
| format | Article |
| id | doaj-art-ec0b2a319d2b499387ed02c351ed4601 |
| institution | OA Journals |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-ec0b2a319d2b499387ed02c351ed46012025-08-20T02:26:45ZengMDPI AGAxioms2075-16802024-10-01131175910.3390/axioms13110759On Analytical Extension of Generalized Hypergeometric Function <sub>3</sub><i>F</i><sub>2</sub>Roman Dmytryshyn0Volodymyra Oleksyn1Faculty of Mathematics and Computer Science, Vasyl Stefanyk Precarpathian National University, 57 Shevchenko Str., 76018 Ivano-Frankivsk, UkraineFaculty of Mathematics and Computer Science, Vasyl Stefanyk Precarpathian National University, 57 Shevchenko Str., 76018 Ivano-Frankivsk, UkraineThe paper considers the generalized hypergeometric function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mmultiscripts><mi>F</mi><mn>2</mn><none></none><mprescripts></mprescripts><mn>3</mn><none></none></mmultiscripts><mo>,</mo></mrow></semantics></math></inline-formula> which is important in various fields of mathematics, physics, and economics. The method is used, according to which the domains of the analytical continuation of the special functions are the domains of convergence of their expansions into a special family of functions, namely branched continued fractions. These expansions have wide domains of convergence and better computational properties, particularly compared with series, making them effective tools for representing special functions. New domains of the analytical continuation of the generalized hypergeometric function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mmultiscripts><mi>F</mi><mn>2</mn><none></none><mprescripts></mprescripts><mn>3</mn><none></none></mmultiscripts></mrow></semantics></math></inline-formula> with real and complex parameters have been established. The paper also includes examples of the presentation and extension of some special functions.https://www.mdpi.com/2075-1680/13/11/759generalized hypergeometric functionbranched continued fractionanalytical continuationconvergenceapproximation by rational functions |
| spellingShingle | Roman Dmytryshyn Volodymyra Oleksyn On Analytical Extension of Generalized Hypergeometric Function <sub>3</sub><i>F</i><sub>2</sub> Axioms generalized hypergeometric function branched continued fraction analytical continuation convergence approximation by rational functions |
| title | On Analytical Extension of Generalized Hypergeometric Function <sub>3</sub><i>F</i><sub>2</sub> |
| title_full | On Analytical Extension of Generalized Hypergeometric Function <sub>3</sub><i>F</i><sub>2</sub> |
| title_fullStr | On Analytical Extension of Generalized Hypergeometric Function <sub>3</sub><i>F</i><sub>2</sub> |
| title_full_unstemmed | On Analytical Extension of Generalized Hypergeometric Function <sub>3</sub><i>F</i><sub>2</sub> |
| title_short | On Analytical Extension of Generalized Hypergeometric Function <sub>3</sub><i>F</i><sub>2</sub> |
| title_sort | on analytical extension of generalized hypergeometric function sub 3 sub i f i sub 2 sub |
| topic | generalized hypergeometric function branched continued fraction analytical continuation convergence approximation by rational functions |
| url | https://www.mdpi.com/2075-1680/13/11/759 |
| work_keys_str_mv | AT romandmytryshyn onanalyticalextensionofgeneralizedhypergeometricfunctionsub3subifisub2sub AT volodymyraoleksyn onanalyticalextensionofgeneralizedhypergeometricfunctionsub3subifisub2sub |