1. Legendre Polynomials Recurrence Relation
the first several Legendre polynomials

2. Legendre Polynomials
the first several Legendre polynomials
Properties

3. Legendre’s DE
Legendre’s DE
Legendre’s DE
solution

4. Legendre Polynomials

5. Legendre’s DE Legendre polynomials Norm Square orthogonal set
is orthogonal with respect to the weight function p(x) = 1 on [ -1, l].
The orthogonality relation
Legendre polynomials
orthogonal set
Norm Square
expanding a function
Fourier series, Fourier cosine series, and Fourier sine series are three ways of expanding a function in terms of an orthogonal set of functions

6. Fourier-Legendre Series
The Fourier-Legendre series of a function defined on the interval (-1, 1) is given by
Example
Write out the first few nonzero terms in the Fourier-Legendre expansion of

7. Fourier-Legendre Series
The Fourier-Legendre series of a function defined on the interval (-1, 1) is given by
Example
Write out the first few nonzero terms in the Fourier-Legendre expansion of

8. Fourier-Legendre Series
The Fourier-Legendre series of a function defined on the interval (-1, 1) is given by
Alternative Form of Series
where