Fractional Generalizations of Rodrigues-Type Formulas for Laguerre Functions in Function Spaces
Generalized Laguerre polynomials, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>L</mi><mi>n</mi><mrow><mo>(</mo><mi>α</mi><mo>)</mo&g...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/9/984 |
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| author | Pedro J. Miana Natalia Romero |
| author_facet | Pedro J. Miana Natalia Romero |
| author_sort | Pedro J. Miana |
| collection | DOAJ |
| description | Generalized Laguerre polynomials, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>L</mi><mi>n</mi><mrow><mo>(</mo><mi>α</mi><mo>)</mo></mrow></msubsup></semantics></math></inline-formula>, verify the well-known Rodrigues’ formula. Using Weyl and Riemann–Liouville fractional calculi, we present several fractional generalizations of Rodrigues’ formula for generalized Laguerre functions and polynomials. As a consequence, we give a new addition formula and an integral representation for these polynomials. Finally, we introduce a new family of fractional Lebesgue spaces and show that some of these special functions belong to them. |
| first_indexed | 2024-03-10T11:54:24Z |
| format | Article |
| id | doaj.art-b0676be38a25476b9357bae9eaf36d60 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T11:54:24Z |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b0676be38a25476b9357bae9eaf36d602023-11-21T17:28:05ZengMDPI AGMathematics2227-73902021-04-019998410.3390/math9090984Fractional Generalizations of Rodrigues-Type Formulas for Laguerre Functions in Function SpacesPedro J. Miana0Natalia Romero1Departamento de Matemáticas, Facultad de Ciencias & IUMA, Universidad de Zaragoza, 50009 Zaragoza, SpainDepartamento de Matemáticas y Computación, Facultad de Ciencia y Tecnología, Universidad de La Rioja, 26006 Logroño, SpainGeneralized Laguerre polynomials, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>L</mi><mi>n</mi><mrow><mo>(</mo><mi>α</mi><mo>)</mo></mrow></msubsup></semantics></math></inline-formula>, verify the well-known Rodrigues’ formula. Using Weyl and Riemann–Liouville fractional calculi, we present several fractional generalizations of Rodrigues’ formula for generalized Laguerre functions and polynomials. As a consequence, we give a new addition formula and an integral representation for these polynomials. Finally, we introduce a new family of fractional Lebesgue spaces and show that some of these special functions belong to them.https://www.mdpi.com/2227-7390/9/9/984Rodrigues’ formulaLaguerre functionsfunction spacesfractional calculus |
| spellingShingle | Pedro J. Miana Natalia Romero Fractional Generalizations of Rodrigues-Type Formulas for Laguerre Functions in Function Spaces Mathematics Rodrigues’ formula Laguerre functions function spaces fractional calculus |
| title | Fractional Generalizations of Rodrigues-Type Formulas for Laguerre Functions in Function Spaces |
| title_full | Fractional Generalizations of Rodrigues-Type Formulas for Laguerre Functions in Function Spaces |
| title_fullStr | Fractional Generalizations of Rodrigues-Type Formulas for Laguerre Functions in Function Spaces |
| title_full_unstemmed | Fractional Generalizations of Rodrigues-Type Formulas for Laguerre Functions in Function Spaces |
| title_short | Fractional Generalizations of Rodrigues-Type Formulas for Laguerre Functions in Function Spaces |
| title_sort | fractional generalizations of rodrigues type formulas for laguerre functions in function spaces |
| topic | Rodrigues’ formula Laguerre functions function spaces fractional calculus |
| url | https://www.mdpi.com/2227-7390/9/9/984 |
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