Spherical harmonics are mathematical functions that represent data on the surface of a sphere. They are used in various fields, including physics, computer graphics, and geophysics, to analyze and visualize spherical data. These functions can describe complex shapes and patterns, making them useful for modeling phenomena like gravitational fields and sound waves. The spherical harmonics are defined by two parameters: degree and order, which determine their shape and orientation. Each function can be visualized as a wave pattern on the sphere, allowing for the decomposition of complex spherical data into simpler components. This makes them essential for tasks such as signal processing and 3D modeling.