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Legendre functions or polynomials is a power series solution of Legendre differential equation about the origin. The series solution converges when satisfies. Equating coefficients gives the desired result.

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This notebook has three objectives: C5 Generalised Fourier Series. Sturm-Liouiville theory does more than guarantee the orthogonality of Legendre polynomials, it also shows that we can represent functions on [? Thus for suitable f x on [?

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