Frobenius & Special Functions · Superchallenge problem

Chebyshev's equation $(1 - x^2)y'' - xy' + 9y = 0$ has a regular singular point at $x = 1$ with indicial roots $0$ and $\tfrac12$. Let $y = \displaystyle\sum_{n\ge0}a_n(1 - x)^{n + 1/2}$, with $a_0 = 1$, be the Frobenius solution about $x = 1$ for the root $\tfrac12$; it converges for $|1 - x| < 2$. Compute $y(0)$. Express your answer in simplest radical form.