(Solution Download) If we multiply the Legendre polynomial of degree n by

If we multiply the Legendre polynomial of degree n by an appropriate scalar we can obtain a polynomial Ln(x) such that Ln( l) = 1 .
(a) Find L0(x), L1 (x), L2 (x), and L3(x).
(b) It can be shown that L"(x) satisfies the recurrence Relation

for all n ? 2. Verify this recurrence for L2(x) and L3(x). Then use it to compute L4(x) and L5(x).

 

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