Question 22.3: Suppose that the general equation for a Legendre polynomial ......

Introduction to Nuclear Reactor Physics [1368692]

Suppose that the general equation for a Legendre polynomial is

(n + 1)P_{n+1}(μ) = (2n + 1)μP_n(μ)  –  nP_{n – 1}(μ)

where the first two polynomials are $P_0(μ) = 1 and P_1(μ) = μ$ . Write out the Legendre polynomials that are needed in a simple $P_3$ approximation in one dimension.

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The $P_3$ approximation involves expanding the angular neutron flux into four terms from N = 0 to N = 3. Therefore, the four Legendre polynomials that are used in this case are

$P_0 = 1$

$P_1 = μ$

$P_2 = \frac{3μ^2 – 1}{2}$

$P_3 = \frac{5μ^3 – 3μ}{2}$

Notice that only the second one is a linear function of μ.

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