The coordinate-free approach to spherical harmonics (original) (raw)
Connection Formulae between Ellipsoidal and Spherical Harmonics with Applications to Fluid Dynamics and Electromagnetic Scattering
Michael Doschoris
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Cartesian Expressions for Surface and Regular Solid Spherical Harmonics Using Binomial Coefficients and Its Use In the Evaluation of Multicenter Integrals
Telhat Ozdogan
Czechoslovak Journal of Physics, 2002
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Electrodynamic spherical harmonic
Andrey Novitsky
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The Triangular Properties of Associated Legendre Functions Using The Vectorial Addition Theorem For Spherical Harmonics
Rami Mehrem
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Transformation between surface spherical harmonic expansion of arbitrary high degree and order and double Fourier series on sphere Toshio Fukushima
Toshio Fukushima
Journal of Geodesy, 2018
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Vector spherical harmonics: Concepts and applications to the single centre expansion method
Nico Sanna
Computer Physics Communications, 2000
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Electronic Supplementary Materials to " Transformation between surface spherical harmonic expansion of arbitrary high degree and order and double Fourier series on sphere "
Toshio Fukushima
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A New Modified Helmholtz Equation for the Expression of the Gravity Gradient and the Intensity of an Electrostatic Field in Spherical Harmonics
Gerassimos Manoussakis
Mathematics, issue 11, 4362, 2023
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Transformation between surface spherical harmonic expansion of arbitrary high degree and order and double Fourier series on sphere
Toshio Fukushima
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Orthogonality of harmonic potentials and fields in spheroidal and ellipsoidal coordinates: application to geomagnetism and geodesy
F. J. Lowes
Geophysical Journal International, 2012
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A computational procedure for obtaining the poles of a spherical harmonic of order N; Application to the multipole expansion of electrostatic interaction
Mihaly Mezei
Journal of Computational Physics, 1976
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On hyperspherical associated Legendre functions: the extension of spherical harmonics to NNN dimensions
Luís Campos
2020
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On the vector solutions of Maxwell equations in spherical coordinate systems
Swarnav Majumder
2022
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Vectorial spherical-harmonics representation of an inhomogeneous elliptically polarized plane wave
Fabrizio Frezza
Journal of the Optical Society of America A, 2015
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Relationships among charges, fields, and potential on spherical surfaces boundary value problems
Ayelet Goldstein
Results in Physics, 2018
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Numerical computation of spherical harmonics of arbitrary degree and order by extending exponent of floating point numbers: II first-, second-, and third-order derivatives
Toshio Fukushima
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Laplace's equation in spherical coordinates and Legendre's equation (I)
James Foadi
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Numerical computation of spherical harmonics of arbitrary degree and order by extending exponent of floating point numbers: III integral
Toshio Fukushima
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New recurrence relations for spherical harmonic functions and their derivatives
Denis Winch
Physics of the Earth and Planetary Interiors, 1968
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3. Homogenous polynomials and spherical harmonics
Anouar Ben Mabrouk
Wavelet Analysis on the Sphere
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On Two Useful Identities in the Theory of Ellipsoidal Harmonics
George Dassios
Studies in Applied Mathematics, 2009
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Spheroidal harmonic expansions for the solution of Laplace's equation for a point source near a sphere
Matt Majic
Physical Review E
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Some integral identities for spherical harmonics in an arbitrary dimension
Kendall Atkinson
Journal of Mathematical Chemistry, 2011
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Spherical Harmonic on a Four Sphere
ASLOOB RATHER
Applied Mathematics and Physics, 2014
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A simple approach to the transformation of spherical harmonic models under coordinate system rotation
Angelo De Santis
Geophysical Journal International, 1996
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Generalized Spherical Harmonics for l=2
Lister Mulindwa
arXiv: Quantum Physics, 2005
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Fourier-series representation and projection of spherical harmonic functions
Jarin Park
Journal of Geodesy, 2012
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New Solution Of Maxwell'S Equations For Spherical Wave
Solomon Khmelnik
2018
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Recursive computation of oblate spheroidal harmonics of the second kind and their first-, second-, and third-order derivatives
Toshio Fukushima
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Novel integral representations for harmonic functions in the interior of a sphere
George Dassios
2009
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An efficient routine for computing symmetric real spherical harmonics for high orders of expansion
Andrzej Kudlicki
Journal of Applied Crystallography, 2005
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Rotation of real spherical harmonics
Guillermo Ramírez
Computer Physics Communications, 1989
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Ultra-high degree spherical harmonic analysis and synthesis using extended-range arithmetic
Kurt Seitz
Journal of Geodesy, 2008
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Numerical computation of spherical harmonics of arbitrary degree and order by extending exponent of floating point numbers
Toshio Fukushima
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Expansion of arbitrary electromagnetic fields in terms of vector spherical wave functions
Antonio Alvaro Ranha Neves
2010
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