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...
Збережено в:
| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2015 |
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2015
|
| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147142 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| 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. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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. |
|---|