Some results for sums of products of Chebyshev and Legendre polynomials

Abstract

Abstract In this paper, we perform a further investigation of the Gegenbauer polynomials, the Chebyshev polynomials of the first and second kinds and the Legendre polynomials. By making use of some analytic and combinatorial methods, we establish some new expressions for sums of products of arbitrary numbers of Chebyshev polynomials of the first and second kinds and Legendre polynomials.

Keywords

• Gegenbauer polynomials
• Chebyshev polynomials
• Legendre polynomials
• Combinatorial identities