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Legendre Polynomials Recurrence Relation

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Presentation on theme: "Legendre Polynomials Recurrence Relation"— Presentation transcript:

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


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