On Legendre numbers
The Legendre numbers, an infinite set of rational numbers are defined from the associated Legendre functions and several elementary properties are presented. A general formula for the Legendre numbers is given. Applications include summing certain series of Legendre numbers and evaluating certain in...
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| Format: | Article |
| Language: | English |
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Wiley
1985-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171285000436 |
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| _version_ | 1832562877222879232 |
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| author | Paul W. Haggard |
| author_facet | Paul W. Haggard |
| author_sort | Paul W. Haggard |
| collection | DOAJ |
| description | The Legendre numbers, an infinite set of rational numbers are defined from the associated Legendre functions and several elementary properties are presented. A general formula for the Legendre numbers is given. Applications include summing certain series of Legendre numbers and evaluating certain integrals. Legendre numbers are used to obtain the derivatives of all orders of the Legendre polynomials at x=1. |
| format | Article |
| id | doaj-art-6d2cdbe1265e4c2eb38dfc26660d3f7a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1985-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-6d2cdbe1265e4c2eb38dfc26660d3f7a2025-02-03T01:21:30ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251985-01-018240741110.1155/S0161171285000436On Legendre numbersPaul W. Haggard0Department of Mathematics, East Carolina University, Greenville 27834, North Carolina, USAThe Legendre numbers, an infinite set of rational numbers are defined from the associated Legendre functions and several elementary properties are presented. A general formula for the Legendre numbers is given. Applications include summing certain series of Legendre numbers and evaluating certain integrals. Legendre numbers are used to obtain the derivatives of all orders of the Legendre polynomials at x=1.http://dx.doi.org/10.1155/S0161171285000436associated Legendre functionsLegendre polynomialsseries of Legendre numbersintegrals of Legendre polynomialsorthogonal setderivatives of Legendre polynomials. |
| spellingShingle | Paul W. Haggard On Legendre numbers International Journal of Mathematics and Mathematical Sciences associated Legendre functions Legendre polynomials series of Legendre numbers integrals of Legendre polynomials orthogonal set derivatives of Legendre polynomials. |
| title | On Legendre numbers |
| title_full | On Legendre numbers |
| title_fullStr | On Legendre numbers |
| title_full_unstemmed | On Legendre numbers |
| title_short | On Legendre numbers |
| title_sort | on legendre numbers |
| topic | associated Legendre functions Legendre polynomials series of Legendre numbers integrals of Legendre polynomials orthogonal set derivatives of Legendre polynomials. |
| url | http://dx.doi.org/10.1155/S0161171285000436 |
| work_keys_str_mv | AT paulwhaggard onlegendrenumbers |