Some Identities and Inequalities Involving Symmetry Sums of Legendre Polynomials

By using the analysis methods and the properties of Chebyshev polynomials of the first kind, this paper studies certain symmetry sums of the Legendre polynomials, and gives some new and interesting identities and inequalities for them, thus improving certain existing results.

[1]  James Wan,et al.  Generating functions of Legendre polynomials: A tribute to Fred Brafman , 2013, J. Approx. Theory.

[2]  Taekyun Kim,et al.  Sums of finite products of Legendre and Laguerre polynomials , 2018, Advances in Difference Equations.

[3]  P. Borwein,et al.  Polynomials and Polynomial Inequalities , 1995 .

[4]  C. Cesarano.  Generalized Chebyshev polynomials , 2014 .

[5]  Mourad E. H. Ismail,et al.  On the generalized Chebyshev polynomials , 1987 .

[6]  Hari M. Srivastava,et al.  The Laguerre and Legendre polynomials from an operational point of view , 2001, Appl. Math. Comput..

[7]  Yuan He.  Some results for sums of products of Chebyshev and Legendre polynomials , 2019, Advances in Difference Equations.

[8]  Zhuoyu Chen,et al.  A New Identity Involving the Chebyshev Polynomials , 2018, Mathematics.

[9]  Somayeh Nemati,et al.  Numerical solution of a class of two-dimensional nonlinear Volterra integral equations using Legendre polynomials , 2013, J. Comput. Appl. Math..

[10]  Shimeng Shen,et al.  Some Types of Identities Involving the Legendre Polynomials , 2019, Mathematics.

[12]  Wang Siyi.  Some new identities of Chebyshev polynomials and their applications , 2015 .

[13]  Md. Shafiqul Islam,et al.  Numerical solutions of eighth order BVP by the Galerkin residual technique with Bernstein and Legendre polynomials , 2015, Appl. Math. Comput..

[14]  Clemente Cesarano.  Identities and generating functions on Chebyshev polynomials , 2012 .

[15]  D. Jackson,et al.  fourier series and orthogonal polynomials , 1943, The Mathematical Gazette.

[16]  Hammad Khalil,et al.  A new method based on Legendre polynomials for solutions of the fractional two-dimensional heat conduction equation , 2014, Comput. Math. Appl..