A family of definite integrals involving Legendre’s polynomials
The main objective of this article is to provide the analytical solutions (not previously found and not available in the literature) of some problems related with definite integrals integrands of which are the products of the derivatives of Legendre’s polynomials of first kind having differ...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Academician Ye.A. Buketov Karaganda University
2023-06-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Online Access: | https://mathematics-vestnik.ksu.kz/apart/2023-110-2/11.pdf |
| _version_ | 1797788615567212544 |
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| author | M.I. Qureshi S.H. Malik D. Ahmad |
| author_facet | M.I. Qureshi S.H. Malik D. Ahmad |
| author_sort | M.I. Qureshi |
| collection | DOAJ |
| description | The main objective of this article is to provide the analytical solutions (not previously found and not available in the literature) of some problems related with definite integrals integrands of which are the products of the derivatives of Legendre’s polynomials of first kind having different order, with the help of some derivatives of Legendre’s polynomials of first kind P_n(x), Rodrigues formula, Leibnitz’s generalized rule for successive integration by parts and certain values of successive differential coefficients of (x^2 − 1)^r at x = ±1. |
| first_indexed | 2024-03-13T01:39:04Z |
| format | Article |
| id | doaj.art-a86222ed29204ec0a914c242363f8bd0 |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-13T01:39:04Z |
| publishDate | 2023-06-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-a86222ed29204ec0a914c242363f8bd02023-07-03T19:16:28ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112023-06-01110211613010.31489/2023M2/116-130A family of definite integrals involving Legendre’s polynomialsM.I. QureshiS.H. MalikD. Ahmad The main objective of this article is to provide the analytical solutions (not previously found and not available in the literature) of some problems related with definite integrals integrands of which are the products of the derivatives of Legendre’s polynomials of first kind having different order, with the help of some derivatives of Legendre’s polynomials of first kind P_n(x), Rodrigues formula, Leibnitz’s generalized rule for successive integration by parts and certain values of successive differential coefficients of (x^2 − 1)^r at x = ±1.https://mathematics-vestnik.ksu.kz/apart/2023-110-2/11.pdf |
| spellingShingle | M.I. Qureshi S.H. Malik D. Ahmad A family of definite integrals involving Legendre’s polynomials Қарағанды университетінің хабаршысы. Математика сериясы |
| title | A family of definite integrals involving Legendre’s polynomials |
| title_full | A family of definite integrals involving Legendre’s polynomials |
| title_fullStr | A family of definite integrals involving Legendre’s polynomials |
| title_full_unstemmed | A family of definite integrals involving Legendre’s polynomials |
| title_short | A family of definite integrals involving Legendre’s polynomials |
| title_sort | family of definite integrals involving legendre s polynomials |
| url | https://mathematics-vestnik.ksu.kz/apart/2023-110-2/11.pdf |
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