Frobenius & Special Functions · Superchallenge problem

The hypergeometric equation $x(1-x)y'' + (2 - 2x)y' - \tfrac14y = 0$ has indicial roots $0$ and $-1$ at $x = 0$. Let $y(x) = \sum_{n\ge0}a_nx^n$ be the Frobenius solution for $r = 0$ with $a_0 = 1$. The series converges at $x = 1$. Compute $y(1)$.