Some Types of Identities Involving the Legendre Polynomials

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.

Keywords

• Legendre polynomials
• recursive sequence
• convolution sums
• combinatorial method
• identity
• polynomial congruence