1. The differential equation (1-2)y" - xy + p²y = 0, where p is a constant, is known as Chebyshev's equation. It can be rewritten in the form I y" + P(x)y+Q(x)y = 0, P(x) = -12 Q(x) = = 1 (a) If P(x) and Q(r) are represented as a power series about 20 = 0, what is the radius of convergence of these power series? (b) Assume that the general solution has the form n=0 an", and find a recurrence for an+2 in terms of an. [Hint: Before plugging back in, multiply through by 1 - x².] (c) Use the recurrence to determine an in terms of ao and a₁, for 2≤ n ≤9. (d) For each pЄ N, there is a unique polynomial solution T,(r) known as the Chebyshev polynomial of degree p. Find T3(x).