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 Ln(x) satisfies the recurrence relation Ln(x) = (2n - 1)/n xLn_1(x) --(n - 1)/n Ln-2(x) for all n>= 2. Verify this recurrence for L2(x) and L3(x). Then use it to compute L4(x) and L5(x).

Answered: If we multiply the Legendre polynomial…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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If we multiply the Legendre polynomial of degree n by an appropriate scalar we can obtain a polynomial L_n(x) such that L_n(l) = 1. (a) Find L₀(x), L₁ (x), L₂(x), and L₃(x). (b) It can be shown that Ln(x) satisfies the recurrence relation L_n(x) = (2n - 1)/n xL_{n_1}(x) --(n - 1)/n L_n-2(x) 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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