5. Consider Legendre equation for a function y(x) defined in the interval -1. Changing the variable y(cos θ) x cos θ in equation (1) derive the trigonometric form of Legendre equation for a function T (0) where 0 θ π: sin θ Then the general solution to (3) is T (0) y(cos θ) AP, (cos0) + BQ, (cos0). 5. Consider Legendre equation for a function y(x) defined in the interval -1. Changing the variable y(cos θ) x cos θ in equation (1) derive the trigonometric form of Legendre equation for a function T (0) where 0 θ π: sin θ Then the general solution to (3) is T (0) y(cos θ) AP, (cos0) + BQ, (cos0).
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