In Physics, Spherical Harmonics are special functions that are used to define the surface of a sphere. Spherical harmonics are important in many theoretical and practical applications. They are most commonly used for solving partial differential equations. They may be used to represent functions defined on the surface of a sphere. They used to represent functions defined on the surface of a sphere similar to how circular functions are used to represent functions on a circle. Spherical harmonics take their simplest form in Cartesian coordinates which obey Laplace's equation.
Spherical harmonics were first investigated in connection with the Newtonian potential of Newton's law of universal gravitation in three dimensions. It was by examining Laplace's equation in spherical coordinates, Thomson and Tait recovered Laplace's spherical harmonics. An alternative definition is that spherical harmonics may be viewed as the angular portion of a set of solutions to Laplace's equation in three dimensions.
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