Some Types of Identities Involving the Legendre Polynomials
In this paper, a new non-linear recursive sequence is firstly introduced. Then, using this sequence, a computational problem involving the convolution of the Legendre polynomial is studied using the basic and combinatorial methods. Finally, we give an interesting identity.
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2019-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/7/2/114 |
| _version_ | 1818509686828171264 |
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| author | Shimeng Shen Li Chen |
| author_facet | Shimeng Shen Li Chen |
| author_sort | Shimeng Shen |
| collection | DOAJ |
| description | In this paper, a new non-linear recursive sequence is firstly introduced. Then, using this sequence, a computational problem involving the convolution of the Legendre polynomial is studied using the basic and combinatorial methods. Finally, we give an interesting identity. |
| first_indexed | 2024-12-10T22:48:47Z |
| format | Article |
| id | doaj.art-8cfc088f2de7448b981da93f9cfb725e |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-10T22:48:47Z |
| publishDate | 2019-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-8cfc088f2de7448b981da93f9cfb725e2022-12-22T01:30:30ZengMDPI AGMathematics2227-73902019-01-017211410.3390/math7020114math7020114Some Types of Identities Involving the Legendre PolynomialsShimeng Shen0Li Chen1School of Mathematics, Northwest University, Xi’an 710069, Shaanxi, ChinaSchool of Mathematics, Northwest University, Xi’an 710069, Shaanxi, ChinaIn this paper, a new non-linear recursive sequence is firstly introduced. Then, using this sequence, a computational problem involving the convolution of the Legendre polynomial is studied using the basic and combinatorial methods. Finally, we give an interesting identity.https://www.mdpi.com/2227-7390/7/2/114Legendre polynomialsrecursive sequenceconvolution sumscombinatorial methodidentitypolynomial congruence |
| spellingShingle | Shimeng Shen Li Chen Some Types of Identities Involving the Legendre Polynomials Mathematics Legendre polynomials recursive sequence convolution sums combinatorial method identity polynomial congruence |
| title | Some Types of Identities Involving the Legendre Polynomials |
| title_full | Some Types of Identities Involving the Legendre Polynomials |
| title_fullStr | Some Types of Identities Involving the Legendre Polynomials |
| title_full_unstemmed | Some Types of Identities Involving the Legendre Polynomials |
| title_short | Some Types of Identities Involving the Legendre Polynomials |
| title_sort | some types of identities involving the legendre polynomials |
| topic | Legendre polynomials recursive sequence convolution sums combinatorial method identity polynomial congruence |
| url | https://www.mdpi.com/2227-7390/7/2/114 |
| work_keys_str_mv | AT shimengshen sometypesofidentitiesinvolvingthelegendrepolynomials AT lichen sometypesofidentitiesinvolvingthelegendrepolynomials |