I am looking for a book reference for the following equation, presenting the coefficients of the Chebyshev polynomials of the second kind:
$$U_n(x)= \sum\limits_{j=0}^{n/2} (-1)^j \binom{n-j}{j}(2x)^{n-2j}$$
Thank you very much, David.
1 Answer
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One of the best books for chebyshev polynomials of the second kind would be "Orthogonal Polynomials" by Gábor Szegó.(“The Chebyshev Polynomials: From Approximation Theory to Algebra and Number Theory”.Is also a good book.)
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$\begingroup$ @David Garber , Is this useful? I can give you some more books. $\endgroup$ Commented Jun 6 at 6:50
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$\begingroup$ I did not find Chebyshev polynomials in Szego's book... I am looking specifically for the equation of the coefficients. I will be happy to have more suggestions for books or survey papers. Thanks $\endgroup$ Commented Jun 6 at 7:38
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$\begingroup$ I found: Higher Transcendental Functions, Vol. 2, p. 185, Equ. 23. Thanks anyway. $\endgroup$ Commented Jun 6 at 7:59