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Mathematics 2019, 7(2), 114; https://doi.org/10.3390/math7020114

Some Types of Identities Involving the Legendre Polynomials

School of Mathematics, Northwest University, Xi’an 710069, Shaanxi, China
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Received: 10 December 2018 / Revised: 18 January 2019 / Accepted: 20 January 2019 / Published: 22 January 2019
(This article belongs to the Special Issue Special Polynomials)
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Abstract

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. View Full-Text
Keywords: Legendre polynomials; recursive sequence; convolution sums; combinatorial method; identity; polynomial congruence Legendre polynomials; recursive sequence; convolution sums; combinatorial method; identity; polynomial congruence
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Shen, S.; Chen, L. Some Types of Identities Involving the Legendre Polynomials. Mathematics 2019, 7, 114.

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