Thread: Solution to Legendre equation in trig form

hey guys,


I've been trying to solve this question,





so the general solution would be


y(cos(theta)) = C Pn(cos(theta)) + D Qn(cos(theta)) right?


and since n = 2 in this case


y(cos(theta)) = C P_2 (cos(theta)) + D Q_2 (cos(theta))


and 0<= theta < 2Pi


But when theta = 0, cos(theta) = 1 and Q_2 is undefined, so D = 0,


so y(cos(theta)) = C P_2 (cos(theta)) = (C/2) (cos^2(theta) - 1)


but


y(cos(0))=y(1) = C P_2(1) = C = ?


So would the 2pi periodic solution be


y(cos(theta)) = (C/2) (cos^2(theta) - 1) ?


Thanks