Answer to Question #179760 in Differential Equations for Barbie

Question

In orthogonality of legendre polynomials, why the limits of integral is from -1 to 1

Answer 1

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In orthogonality of legendre polynomials, the limits of integral is from -1 to 1 as

$\bull$ [ -1,1] is the classical finite interval on which ops are defined.

$\bull$ The Lagrange polynomials are also popular, which are based on Legendre or Chebyshev polynomials.

$\bull$ Legendre and Chebyshev polynomials are known orthogonal polynomials in [-1,1]. However, due to their least(minimum) error property the Chebyshev polynomials are frequently used in applications.

$\bull$ Legendre and Chebyshev polynomials appear very frequently in applications.

$\bull$ B splines(but they should be orthogonalized by gram Schmidt procedure and fit to [-1,1])

$\bigstar$ These are the few reasons for

orthogonality of legendre polynomials, the limits of integral is from -1 to 1 as