Orthogonal Polynomials and Related Special Functions Applied in Geosciences and Engineering Computations
In applications of mathematics involving either the Laplace or the Helmholtz equation in spherical coordinates the associated Legendre equation occurs. Its solutions are called associated Legendre functions. They have some relations to classical Legendre orthogonal polynomials and classical Jacobi o...
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| Format: | Article |
| Language: | English |
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University of Žilina
2010-03-01
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| Series: | Communications |
| Subjects: | |
| Online Access: | https://komunikacie.uniza.sk/artkey/csl-201001-0002_orthogonal-polynomials-and-related-special-functions-applied-in-geosciences-and-engineering-computations.php |
| _version_ | 1797847045161091072 |
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| author | Vladimir Guldan Mariana Marcokova |
| author_facet | Vladimir Guldan Mariana Marcokova |
| author_sort | Vladimir Guldan |
| collection | DOAJ |
| description | In applications of mathematics involving either the Laplace or the Helmholtz equation in spherical coordinates the associated Legendre equation occurs. Its solutions are called associated Legendre functions. They have some relations to classical Legendre orthogonal polynomials and classical Jacobi orthogonal polynomials. The classical Legendre polynomials and the associated Legendre functions have been used by some authors at the approximation of length of curves and cylindrical surfaces and the approximation of Earth shape in geosciences and engineering computations. In the present paper we investigate some relations between these functions pointing out possible applications in geosciences. |
| first_indexed | 2024-04-09T18:04:23Z |
| format | Article |
| id | doaj.art-a16f0072408a49168ba2a524774b1c4f |
| institution | Directory Open Access Journal |
| issn | 1335-4205 2585-7878 |
| language | English |
| last_indexed | 2024-04-09T18:04:23Z |
| publishDate | 2010-03-01 |
| publisher | University of Žilina |
| record_format | Article |
| series | Communications |
| spelling | doaj.art-a16f0072408a49168ba2a524774b1c4f2023-04-14T06:30:17ZengUniversity of ŽilinaCommunications1335-42052585-78782010-03-01121121510.26552/com.C.2010.1.12-15csl-201001-0002Orthogonal Polynomials and Related Special Functions Applied in Geosciences and Engineering ComputationsVladimir Guldan0Mariana Marcokova1Department of Mathematics, Faculty of Science, University of Zilina, SlovakiaDepartment of Mathematics, Faculty of Science, University of Zilina, SlovakiaIn applications of mathematics involving either the Laplace or the Helmholtz equation in spherical coordinates the associated Legendre equation occurs. Its solutions are called associated Legendre functions. They have some relations to classical Legendre orthogonal polynomials and classical Jacobi orthogonal polynomials. The classical Legendre polynomials and the associated Legendre functions have been used by some authors at the approximation of length of curves and cylindrical surfaces and the approximation of Earth shape in geosciences and engineering computations. In the present paper we investigate some relations between these functions pointing out possible applications in geosciences.https://komunikacie.uniza.sk/artkey/csl-201001-0002_orthogonal-polynomials-and-related-special-functions-applied-in-geosciences-and-engineering-computations.phpno keywords |
| spellingShingle | Vladimir Guldan Mariana Marcokova Orthogonal Polynomials and Related Special Functions Applied in Geosciences and Engineering Computations Communications no keywords |
| title | Orthogonal Polynomials and Related Special Functions Applied in Geosciences and Engineering Computations |
| title_full | Orthogonal Polynomials and Related Special Functions Applied in Geosciences and Engineering Computations |
| title_fullStr | Orthogonal Polynomials and Related Special Functions Applied in Geosciences and Engineering Computations |
| title_full_unstemmed | Orthogonal Polynomials and Related Special Functions Applied in Geosciences and Engineering Computations |
| title_short | Orthogonal Polynomials and Related Special Functions Applied in Geosciences and Engineering Computations |
| title_sort | orthogonal polynomials and related special functions applied in geosciences and engineering computations |
| topic | no keywords |
| url | https://komunikacie.uniza.sk/artkey/csl-201001-0002_orthogonal-polynomials-and-related-special-functions-applied-in-geosciences-and-engineering-computations.php |
| work_keys_str_mv | AT vladimirguldan orthogonalpolynomialsandrelatedspecialfunctionsappliedingeosciencesandengineeringcomputations AT marianamarcokova orthogonalpolynomialsandrelatedspecialfunctionsappliedingeosciencesandengineeringcomputations |