Question

1. The Legendre polynomials Pn(x), n = 0, 1, … are defined recursively as follows

nPn(x) = (2n-1)xPn -1 – (n-1)Pn-2(x), n = 2, 3, … , P0(x) = 1, P1(x) = x

a) Write MATLAB function P = LegendP(n) that takes an integer n (the degree of Pn(x)) and returns its coefficient stored in the descending order of powers.
b) Plot all Legendre polynomials Pn(x), n = 0, 1, …,6 over the interval [-1,1] in one figure.

Answer 1

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