Analyzing, developing and exploiting results obtained by Laplace in 1785 on the Fourier-series expansion of the function (1−2αcosθ+α2)−s, we obtain a family of new expansions and generating functions for the Chebyshev polynomials. A relation between the generating functions of the Chebyshev polynomials Tn and the Gegenbauer polynomials Cn(2) is given.
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Brezinski et al. (2024) studied this question.
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