32.28. Calculate the Chebyshev polynomials $T_{n}(x)$ for $n \leqslant 5$.

Compute the Chebyshev polynomials $T_{n}(x)$ for $n \leqslant 5$.
32.28. Answer: $T_{1}(x)=x, T_{2}(x)=2 x^{2}-1, T_{3}(x)=4 x^{3}-3 x$, $T_{4}(x)=8 x^{4}-8 x^{2}+1, T_{5}(x)=16 x^{5}-20 x^{3}+5 x$.