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He, Yuan

Some results for sums of products of Chebyshev and Legendre polynomials. (English) Zbl 1485.33008

Adv. Difference Equ. 2019, Paper No. 357, 13 p. (2019).
Summary: 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.

MSC:

33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
11B83 Special sequences and polynomials
11B39 Fibonacci and Lucas numbers and polynomials and generalizations

Keywords:

Gegenbauer polynomials; Chebyshev polynomials; Legendre polynomials; combinatorial identities
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References:

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