The Legendre polynomials play an important role in mathematical physics. For example, in

Chapter 5, Problem 20

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The Legendre polynomials play an important role in mathematical physics. For example, in solving Laplaces equation (the potential equation) in spherical coordinates, we encounter the equation d2F() d2 + cot dF() d + n(n + 1) F() = 0, 0 < < , where n is a positive integer. Show that the change of variable x = cos leads to the Legendre equation with = n for y = f ( x) = F(arccos x).

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