Hi am trying to prove using the recursive formula that the legendre polynomial P3(x)=(1/2)*(5x^3 - 3x) .......(1)
This is the recursive formula
where P2=(1/2)(3x^2 - 1) and P1=x
we have chosen k=2 so it gives Pk+1 = P3.
Everytime I try to evaluate this by hand, I dont get equation (1), which is what I need, can someone help me on this.
I even tried matlab which gave an ans = 45/4*x^3-27/4*x, which is still not (1).