The Legendre Polynomials in Closed Form

We use the recursion relationship for the the coefficients of the power series solution to the Legendre differential equation ( • The Legendre Different... ) to find a closed form for the Legendre polynomials. While the closed form may appear slightly complex, it will be important to know the exact coefficients when dealing with problems in electrostatics or gravitation. We express the polynomials in descending powers of x.
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[@skapun7744]

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[@mikethemathematician]

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