Fractional Integral and Generalized Stieltjes Transforms for Hypergeometric Functions as Transmutation Operators
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Fractional Integral and Generalized Stieltjes Transforms for Hypergeometric Functions as Transmutation Operators
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| Creator |
Koornwinder, T.H.
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| 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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| Date |
2019-02-13T17:26:00Z
2019-02-13T17:26:00Z 2015 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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