Show up when solving the Laplace's equation on spherical coordinates by separation of variables, which leads to the differential equation shown at: en.wikipedia.org/w/index.php?title=Legendre_polynomials&oldid=1018881414#Definition_via_differential_equation.
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Legendre polynomials are a sequence of orthogonal polynomials that arise in various fields of mathematics and physics, particularly in solving problems that involve spherical coordinates, such as potential theory, quantum mechanics, and electrodynamics. They are named after the French mathematician Adrien-Marie Legendre.