Chapter 12.23, Problem 23MP

Solve by power series $\left(1-x^2\right)y^{\prime \prime }-x{y}^{\prime }+n^{2}y=0.$ The polynomial solutions of this equation with coefficients determined to make $y(1)=1$ are called Chebyshev polynomials $T_n(x).$ Find $T_0,T_1,$ and $T_2$.