The Legendre polynomials Pn(x)P_n(x)Pn(x) satisfy: (n+1)Pn+1(x)=(2n+1)xPn(x)−nPn−1(x)(n+1)P_{n+1}(x) = (2n+1)xP_n(x) - nP_{n-1}(x)(n+1)Pn+1(x)=(2n+1)xPn(x)−nPn−1(x) with P0(x)=1,P1(x)=xP_0(x) = 1, P_1(x) = xP0(x)=1,P1(x)=x. Compute P2(1)P_2(1)P2(1).
1
32\frac{3}{2}23
2
52\frac{5}{2}25