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Unformatted text preview: MATH 405: Quiz 7 Name: November 6, 2006 1 1. Given that the first 4 Legendre polynomials are P0 = 1, P1 = x, P2 = 2 (3x2  1), and 1 3 2 P3 = 2 (5x  3x), represent the function f (x) = 2x as a Legendre expansion. 2. Consider a SturmLiouville equation for y(x) in the standard form d dx P (x) dy dx + Q(x)y = R(x)y on the interval (0, 12) with P = x, Q = 5x2 , and R = x3 + 12. Given an arbitrary function g also defined on (0,12), which we can expand as g(x) = an yn (x), how would you determine the an ? Write an explicit formula in terms of the eigenfunctions yn . ...
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 Fall '06
 BELMONTE
 Calculus, Polynomials

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