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High Quality Content by WIKIPEDIA articles! This is a table of orthonormalized spherical harmonics that employ the Condon-Shortley phase up to degree l=10. Some of these formulas give the "Cartesian" version. This assumes x, y, z, and r are related to and varphi, through the usual spherical-to-Cartesian coordinate transformation. In mathematics, the spherical harmonics are the angular portion of a set of solutions to Laplace's equation. Represented in a system of spherical coordinates, Laplace's spherical harmonics Y_ell^m are a specific set of spherical harmonics that forms an orthogonal system, first introduced by Pierre Simon de Laplace. Spherical harmonics are important in many theoretical and practical applications, particularly in the computation of atomic orbital electron configurations, representation of gravitational fields, geoids, and the magnetic fields of planetary bodies and stars, and characterization of the cosmic microwave background radiation.