The Laguerre polynomials L0(x) = 1, L1(x) = 1 x, L2(x) = x2 4x + 2, and L3(x) = x3 + 9x2
Chapter 4, Problem 7(choose chapter or problem)
The Laguerre polynomials L0(x) = 1, L1(x) = 1 x, L2(x) = x2 4x + 2, and L3(x) = x3 + 9x2 18x + 6 are derived in Exercise 11 of Section 8.2. As shown in Exercise 6, these polynomials are useful in approximating integrals of the form 0 ex f (x) dx = 0. a. Derive the quadrature formula using n = 2 and the zeros of L2(x). b. Derive the quadrature formula using n = 3 and the zeros of L3(x).
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