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  1. Show that:
  2. $T_n'(x)$=$2n\sum_{k=0\\k+n~~odd}^{n-1}\frac{1}{c_k}T_k(x)$

  3. $T_n''(x)$=$\sum_{k=0\\k+n even}^{n-2}\frac{1}{c_k}n(n^2-k^2)T_k(x)$ where $c_0=2$ and $c_n=1$ for $n\geq1$


I tried using the differential recursive relation of chebyshev polynomials but was unable to establish a relation that would help me solve the problem.

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  • $\begingroup$ For which values of n have you manually verified the equations? Sometime you will see a pattern or catch an error in the text. $\endgroup$ – Carl Christian Apr 24 at 11:59
  • $\begingroup$ I was able to to use the recursive differential equation to show for the 1st order derivative. but i've not been able to identify one such method for the second one $\endgroup$ – Santa Apr 24 at 12:04

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