The lth Legendre polynomial is given by P(x) These satisfy Legendre's equation ((1 − x²) P{(x))' + l(l + 1)P₁(x) = 0. Use this and integration by parts to show that 1 P₁(x)P₁(x) dx = = 2 21 + 1* = d 1 1!2¹ dx¹ ; (x² − 1)². -

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