Some applications of Legendre numbers
The associated Legendre functions are defined using the Legendre numbers. From these the associated Legendre polynomials are obtained and the derivatives of these polynomials at x=0 are derived by using properties of the Legendre numbers. These derivatives are then used to expand the associated Lege...
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| Format: | Article |
| Language: | English |
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Wiley
1988-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171288000481 |
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| _version_ | 1832545410786263040 |
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| author | Paul W. Haggard |
| author_facet | Paul W. Haggard |
| author_sort | Paul W. Haggard |
| collection | DOAJ |
| description | The associated Legendre functions are defined using the Legendre numbers. From these the associated Legendre polynomials are obtained and the derivatives of these polynomials at x=0 are derived by using properties of the Legendre numbers. These derivatives are then used to expand the associated Legendre polynomials and xn in series of Legendre polynomials. Other applications include evaluating certain integrals, expressing polynomials as linear combinations of Legendre polynomials, and expressing linear combinations of Legendre polynomials as polynomials. A connection between Legendre and Pascal numbers is also given. |
| format | Article |
| id | doaj-art-f172c93933544399bb47668674e8f174 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1988-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-f172c93933544399bb47668674e8f1742025-02-03T07:25:55ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251988-01-0111240541210.1155/S0161171288000481Some applications of Legendre numbersPaul W. Haggard0Department of Mathematics, East Carolina University, Greenville 27858, North Carolina, USAThe associated Legendre functions are defined using the Legendre numbers. From these the associated Legendre polynomials are obtained and the derivatives of these polynomials at x=0 are derived by using properties of the Legendre numbers. These derivatives are then used to expand the associated Legendre polynomials and xn in series of Legendre polynomials. Other applications include evaluating certain integrals, expressing polynomials as linear combinations of Legendre polynomials, and expressing linear combinations of Legendre polynomials as polynomials. A connection between Legendre and Pascal numbers is also given.http://dx.doi.org/10.1155/S0161171288000481associated Legendre functions and polynomialsLegendre polynomialsderivatives of associated Legendre polynomialsseries and integrals of Legendre polynomialsLegendre and Pascal numbers. |
| spellingShingle | Paul W. Haggard Some applications of Legendre numbers International Journal of Mathematics and Mathematical Sciences associated Legendre functions and polynomials Legendre polynomials derivatives of associated Legendre polynomials series and integrals of Legendre polynomials Legendre and Pascal numbers. |
| title | Some applications of Legendre numbers |
| title_full | Some applications of Legendre numbers |
| title_fullStr | Some applications of Legendre numbers |
| title_full_unstemmed | Some applications of Legendre numbers |
| title_short | Some applications of Legendre numbers |
| title_sort | some applications of legendre numbers |
| topic | associated Legendre functions and polynomials Legendre polynomials derivatives of associated Legendre polynomials series and integrals of Legendre polynomials Legendre and Pascal numbers. |
| url | http://dx.doi.org/10.1155/S0161171288000481 |
| work_keys_str_mv | AT paulwhaggard someapplicationsoflegendrenumbers |