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Everything about Spherical harmonics
Special mathematical functions defined on the surface of a sphere
In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often employed in solving partial differential equations in many scientific fields. The table of spherical harmonics contains a list of common spherical harmonics. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Spherical harmonicsA 5-minute orientation
- Skim a recent paper: SPHARM-Net: Spherical Harmonics-Based Convolution for Cortical ParcellationInfluential work since 2022
- Pick up a classic book: Spherical harmonicsThe most-reprinted book on the subject
- Read the landmark paper: healpy: equal area pixelization and spherical harmonics transforms for data on the sphere in PythonCited 973 times
- Go sideways: Spin-weighted spherical harmonicsA closely related topic
- Go sideways: Associated Legendre polynomialsA closely related topic
📖 Definitions
Noun The solutions to Laplace's equation using spherical coordinates
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
healpy: equal area pixelization and spherical harmonics transforms for data on the sphere in Python
Spin- s Spherical Harmonics and ð
Oscillatory integrals and spherical harmonics
Spherical Harmonics
Spherical Harmonics
Odd-parity bipolar spherical harmonics
Importance Sampling Spherical Harmonics
Regularization of spherical cap harmonics
🆕 Influential since 2022
SPHARM-Net: Spherical Harmonics-Based Convolution for Cortical Parcellation
4D reconstruction of murine developmental trajectories using spherical harmonics
Fast evaluation of spherical harmonics with sphericart
A Spherical Harmonics Decomposition Method (SHDM) for Irregular Matrix Coils Design
Gravity degree–depth relationship using point mass spherical harmonics
📚 Books worth reading
Spherical harmonicsThomas Murray MacRobert · 1927
The theory of spherical and ellipsoidal harmonicsErnest William Hobson · 1931- 📕Spherical harmonicsThomas Murray MacRobert · 1927
- 📕Geometric Applications of Fourier Series and Spherical HarmonicsHelmut Groemer · 1996
Fundamentals of Spherical Array ProcessingBoaz Rafaely · 2015- 📕The hypergeometric and Legendre functions with applications to integral equations of potential theoryChester Snow · 1942
An elementary treatise on spherical harmonics and subjects connected with themNorman Macleod Ferrers · 1877
Handbuch der KugelfunctionenEduard Heine · 1861
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Spin-weighted spherical harmonics In special functions, a topic in mathematics, spin-weighted spherical harmonics are generalizations of the standard spherical harmonics and—like the usual…
- Associated Legendre polynomials In mathematics, the associated Legendre polynomials are the canonical solutions of the general Legendre differential equation (1−x2)d2dx2Pℓm(x)−2xddxP…
- Solid harmonics In physics and mathematics, the solid harmonics are solutions of the Laplace equation in spherical polar coordinates, assumed to be (smooth) functions…
- Laplace's equation In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its…
- Legendre polynomials In mathematics, Legendre polynomials, named after Adrien-Marie Legendre (1782), are a system of complete and orthogonal polynomials with a wide number…
- Zonal spherical harmonics In the mathematical study of rotational symmetry, the zonal spherical harmonics are special spherical harmonics that are invariant under the rotation through…
- Vector spherical harmonics In mathematics, vector spherical harmonics (VSH) are an extension of the scalar spherical harmonics for use with vector fields. The components of the VSH…
- Spherical multipole moments In physics, spherical multipole moments are the coefficients in a series expansion of a potential that varies inversely with the distance R to a source…