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Everything about Harmonic function
Functions in mathematics
In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function , where is an open subset of , that satisfies Laplace's equation, that is, everywhere on . This is usually written as or Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Harmonic functionA 5-minute orientation
- Skim a recent paper: Distributed harmonic patterns of structure-function dependence orchestrate human consciousnessInfluential work since 2022
- Pick up a classic book: A course of modern analysisThe most-reprinted book on the subject
- Read the landmark paper: Harmonic Vibrational Frequencies: An Evaluation of Hartree−Fock, Møller−Plesset, Quadratic Configuration Interaction, Density Functional Theory, and Semiempirical Scale FactorsCited 6,472 times
- Go sideways: Gradient discretisation methodA closely related topic
- Go sideways: Spherical meanA closely related topic
📖 Definitions
Noun A function of two, three or n variables which is a solution to any of Laplace's equations
🏆 Landmark papers (most cited)
Harmonic Vibrational Frequencies: An Evaluation of Hartree−Fock, Møller−Plesset, Quadratic Configuration Interaction, Density Functional Theory, and Semiempirical Scale Factors
Stochastic Harmonic Function Representation of Stochastic Processes
Inverter harmonic reduction using Walsh function harmonic elimination method
Modified harmonic Robin function
The empirical harmonic potential function of diborane
On Stein-Weiss conjugate harmonic function and Octonion analytic function
Harmonic oscillator with a δ-function potential
Harmonic Function in Rock Music
🆕 Influential since 2022
Distributed harmonic patterns of structure-function dependence orchestrate human consciousness
Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system
Cropland Change Detection With Harmonic Function and Generative Adversarial Network
On M. Riesz Conjugate Function Theorem for Harmonic Functions
Harmonic Function for 3D Warped Transition Geometry and Its Practical Use
📚 Books worth reading
A course of modern analysisE. T. Whittaker, G. N. Watson · 1902- 📕Leçons d'analyse fonctionnelleFrigyes Riesz · 1952
Complex variablesFrancis J. Flanigan · 1972
Spherical harmonicsThomas Murray MacRobert · 1927
Studies on the origin of harmonic tonalityCarl Dahlhaus · 1990
A treatise on attractions, Laplace's functions and the figure of the earthPratt, John Henry · 1861
The theory of spherical and ellipsoidal harmonicsErnest William Hobson · 1931
Leçons d'analyse fonctionelleFrigyes Riesz · 1955
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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