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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| Дата: | 2015 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2015
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147142 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147142 |
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irk-123456789-1471422019-02-14T01:25:34Z Fractional Integral and Generalized Stieltjes Transforms for Hypergeometric Functions as Transmutation Operators Koornwinder, T.H. 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. 2015 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147142 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Koornwinder, T.H. |
| spellingShingle |
Koornwinder, T.H. Fractional Integral and Generalized Stieltjes Transforms for Hypergeometric Functions as Transmutation Operators Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Koornwinder, T.H. |
| author_sort |
Koornwinder, T.H. |
| title |
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_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_sort |
fractional integral and generalized stieltjes transforms for hypergeometric functions as transmutation operators |
| publisher |
Інститут математики НАН України |
| publishDate |
2015 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147142 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT koornwinderth fractionalintegralandgeneralizedstieltjestransformsforhypergeometricfunctionsastransmutationoperators |
| first_indexed |
2023-05-20T17:26:41Z |
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2023-05-20T17:26:41Z |
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1796153310132043776 |