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Program 1
Legendre Polynomial
Plot of Legendre polynomials
Output 1
Program 2
Legendre Polynomial
Recurrence relation of Legendre Polynomial
$$ \small (1 - x^2) P_n'(x) = (n + 1) x P_n(x) - (n + 1) P_{n+1}(x) $$
Output 2