Differential Equations Solutions
Legendre polynomials are a sequence of orthogonal polynomials that arise in solving certain types of differential equations, particularly in the context of spectral methods for approximating solutions. These polynomials, denoted as $$P_n(x)$$, play a critical role in expanding functions in terms of orthogonal bases and are commonly used in numerical analysis, especially for problems defined on the interval [-1, 1]. Their orthogonality property allows for efficient function representation and approximation.
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