Multi-Integral Representations for Associated Legendre and Ferrers Functions
For the associated Legendre and Ferrers functions of the first and second kind, we obtain new multi-derivative and multi-integral representation formulas. The multi-integral representation formulas that we derive for these functions generalize some classical multi-integration formulas. As a result o...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-09-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/12/10/1598 |
| _version_ | 1797552567991926784 |
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| author | Howard S. Cohl Roberto S. Costas-Santos |
| author_facet | Howard S. Cohl Roberto S. Costas-Santos |
| author_sort | Howard S. Cohl |
| collection | DOAJ |
| description | For the associated Legendre and Ferrers functions of the first and second kind, we obtain new multi-derivative and multi-integral representation formulas. The multi-integral representation formulas that we derive for these functions generalize some classical multi-integration formulas. As a result of the determination of these formulae, we compute some interesting special values and integral representations for certain particular combinations of the degree and order, including the case where there is symmetry and antisymmetry for the degree and order parameters. As a consequence of our analysis, we obtain some new results for the associated Legendre function of the second kind, including parameter values for which this function is identically zero. |
| first_indexed | 2024-03-10T16:02:57Z |
| format | Article |
| id | doaj.art-a13f722af92c42caa269fc392268844e |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T16:02:57Z |
| publishDate | 2020-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-a13f722af92c42caa269fc392268844e2023-11-20T15:09:04ZengMDPI AGSymmetry2073-89942020-09-011210159810.3390/sym12101598Multi-Integral Representations for Associated Legendre and Ferrers FunctionsHoward S. Cohl0Roberto S. Costas-Santos1Applied and Computational Mathematics Division, National Institute of Standards and Technology, Mission Viejo, CA 92694, USADepartamento de Física y Matemáticas, Universidad de Alcalá, c.p. 28871 Alcalá de Henares, SpainFor the associated Legendre and Ferrers functions of the first and second kind, we obtain new multi-derivative and multi-integral representation formulas. The multi-integral representation formulas that we derive for these functions generalize some classical multi-integration formulas. As a result of the determination of these formulae, we compute some interesting special values and integral representations for certain particular combinations of the degree and order, including the case where there is symmetry and antisymmetry for the degree and order parameters. As a consequence of our analysis, we obtain some new results for the associated Legendre function of the second kind, including parameter values for which this function is identically zero.https://www.mdpi.com/2073-8994/12/10/1598associated legendre functionsferrers functionsintegral representationsgauss hypergeometric function |
| spellingShingle | Howard S. Cohl Roberto S. Costas-Santos Multi-Integral Representations for Associated Legendre and Ferrers Functions Symmetry associated legendre functions ferrers functions integral representations gauss hypergeometric function |
| title | Multi-Integral Representations for Associated Legendre and Ferrers Functions |
| title_full | Multi-Integral Representations for Associated Legendre and Ferrers Functions |
| title_fullStr | Multi-Integral Representations for Associated Legendre and Ferrers Functions |
| title_full_unstemmed | Multi-Integral Representations for Associated Legendre and Ferrers Functions |
| title_short | Multi-Integral Representations for Associated Legendre and Ferrers Functions |
| title_sort | multi integral representations for associated legendre and ferrers functions |
| topic | associated legendre functions ferrers functions integral representations gauss hypergeometric function |
| url | https://www.mdpi.com/2073-8994/12/10/1598 |
| work_keys_str_mv | AT howardscohl multiintegralrepresentationsforassociatedlegendreandferrersfunctions AT robertoscostassantos multiintegralrepresentationsforassociatedlegendreandferrersfunctions |