Fractional Integral and Generalized Stieltjes Transforms for Hypergeometric Functions as Transmutation Operators
For each of the eight n-th derivative parameter changing formulas for Gauss hypergeometric functions a corresponding fractional integration formula is given. For both types of formulas the differential or integral operator is intertwining between two actions of the hypergeometric differential operat...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2015 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147142 |
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| Cite this: | Fractional Integral and Generalized Stieltjes Transforms for Hypergeometric Functions as Transmutation Operators / T.H. Koornwinder // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 26 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862635371743936512 |
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| author | Koornwinder, T.H. |
| author_facet | Koornwinder, T.H. |
| citation_txt | Fractional Integral and Generalized Stieltjes Transforms for Hypergeometric Functions as Transmutation Operators / T.H. Koornwinder // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 26 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | For each of the eight n-th derivative parameter changing formulas for Gauss hypergeometric functions a corresponding fractional integration formula is given. For both types of formulas the differential or integral operator is intertwining between two actions of the hypergeometric differential operator (for two sets of parameters): a so-called transmutation property. This leads to eight fractional integration formulas and four generalized Stieltjes transform formulas for each of the six different explicit solutions of the hypergeometric differential equation, by letting the transforms act on the solutions. By specialization two Euler type integral representations for each of the six solutions are obtained.
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| first_indexed | 2025-11-30T17:43:12Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147142 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-30T17:43:12Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Koornwinder, T.H. 2019-02-13T17:26:00Z 2019-02-13T17:26:00Z 2015 Fractional Integral and Generalized Stieltjes Transforms for Hypergeometric Functions as Transmutation Operators / T.H. Koornwinder // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 26 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33C05; 44A15; 44A20; 26A33 DOI:10.3842/SIGMA.2015.074 https://nasplib.isofts.kiev.ua/handle/123456789/147142 For each of the eight n-th derivative parameter changing formulas for Gauss hypergeometric functions a corresponding fractional integration formula is given. For both types of formulas the differential or integral operator is intertwining between two actions of the hypergeometric differential operator (for two sets of parameters): a so-called transmutation property. This leads to eight fractional integration formulas and four generalized Stieltjes transform formulas for each of the six different explicit solutions of the hypergeometric differential equation, by letting the transforms act on the solutions. By specialization two Euler type integral representations for each of the six solutions are obtained. This paper is a contribution to the Special Issue on Exact Solvability and Symmetry Avatars in honour of
 Luc Vinet. The full collection is available at http://www.emis.de/journals/SIGMA/ESSA2014.html.
 I am very grateful to Sergei Sitnik for his comments, in particular about Letnikov’s paper [14]
 from 1874. Thanks also to Dmitry Karp for helpful comments. Furthermore, the paper took
 profit from comments and lists of typos in referees’ reports. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Fractional Integral and Generalized Stieltjes Transforms for Hypergeometric Functions as Transmutation Operators Article published earlier |
| spellingShingle | Fractional Integral and Generalized Stieltjes Transforms for Hypergeometric Functions as Transmutation Operators Koornwinder, T.H. |
| title | Fractional Integral and Generalized Stieltjes Transforms for Hypergeometric Functions as Transmutation Operators |
| title_full | Fractional Integral and Generalized Stieltjes Transforms for Hypergeometric Functions as Transmutation Operators |
| title_fullStr | Fractional Integral and Generalized Stieltjes Transforms for Hypergeometric Functions as Transmutation Operators |
| title_full_unstemmed | Fractional Integral and Generalized Stieltjes Transforms for Hypergeometric Functions as Transmutation Operators |
| title_short | Fractional Integral and Generalized Stieltjes Transforms for Hypergeometric Functions as Transmutation Operators |
| title_sort | fractional integral and generalized stieltjes transforms for hypergeometric functions as transmutation operators |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147142 |
| work_keys_str_mv | AT koornwinderth fractionalintegralandgeneralizedstieltjestransformsforhypergeometricfunctionsastransmutationoperators |