# ICE: Matlab Flow

Recall that the three-term recurrence relation for Chebyshev polynomials is given by $T_{k+1}(x) = 2xT_k(x)-T_{k-1}(x),$ where we know that $$T_0(x) = 1,$$ and $$T_1(x)=x,$$ for $$x\in[-1,1].$$ Given some maximal degree $$K$$ that we choose, write a script that uses this relation to generate a $$(K+1)\times N$$ array T whose $$k^\text{th}$$ row comprises the values of $$T_{k-1}$$ at some vector $$x$$ of length $$N$$, which you provide. In other words, T(k+1,n)$$=T_k(x_n)$$ for $$k=0,1,\dots,K$$ and $$n=1,2,\dots,N$$. Your script should then plot the rows of T.

A solution for the final is available.

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