Let $T_n$ and $U_n$ denote the Chebyshev polynomials of first and second kind. Show that $T_n''(x) = nfrac{(n+1)T_n(x) - U_n(x)}{x^2 - 1}, quad x eq pm 1.$
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We can use the recurrence relations for Tn(z) and Un(z) to simplify this expression: (n + 1)Tn(z) - Un(2)T"(z) Show more…
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