Frobenius & Special Functions · Medium problem

Using the Legendre recurrence $(n+1)P_{n+1}(x) = (2n+1)xP_n(x) - nP_{n-1}(x)$ with $P_0 = 1$ and $P_1 = x$, compute $P_4\!\left(\tfrac12\right)$. Express your answer as a common fraction.