Revision #926 → #1581 · back to history
addedSpherical harmonicsb6f48787aabb
addedHarmonic functions818b3e5c510d
addedLaplace's spherical harmonicse4242a4c853a
addedLegendre expansion of Newtonian potential19daa7bacd9c
addedSolid spherical harmonics (Thomson–Tait)993d64633eb4
addedLaplace's equation in spherical coordinates5eec8f2c85a7
addedSeparation of variables for Laplace's equatione19bbc86b1d0
addedSpherical harmonic function of degree ℓ and order m39f5567b99fa
addedGeneral solution to Laplace's equation in a ball3eca8d97cbe3
addedSpherical harmonics as eigenfunctions of L^26f5615029987
addedEigenvalue λ = ℓ(ℓ+1) via raising/lowering operatorsde2fc2d116ab
addedHomogeneous polynomial of degree ℓ3d1b7bc1ecef
addedHarmonic polynomial4ebee9c444bc
addedSpherical harmonics as restrictions of harmonic polynomialsf09b8a272a45
addedLinear functions as harmonic polynomials of degree 1ea7a00680d4b
addedSpherical harmonic from a homogeneous polynomial8422632d3b64
addedCondon–Shortley phase37370dee2197
addedOrthonormal complex spherical harmonics5d24f23ba3d8
addedOrthonormality relation for spherical harmonics78d743bd93bd
addedSchmidt semi-normalized harmonics64a363a30b48
addedComplex conjugation relation503f5a5576d7
addedReal spherical harmonicsc3de14a8f721
addedTesseral spherical harmonicse01eafbbc3b3
addedReal p functions in quantum chemistrydcf6e00417c8
addedSolid harmonics as basis of harmonic homogeneous polynomialsdada184e77d5
addedHerglotz generating function1b1c06b858ca
addedNull property of the Herglotz vectorbad0813e189c
addedSpherical tensor operatorsde09661ab407
addedSeparated Cartesian form8bf7f5b69f14
addedExplicit Cartesian spherical harmonic examples9ac4e6963f76
addedReal Cartesian spherical harmonics1f483f7f945f
addedReduction to Legendre polynomials when m=0b4d0586c5d9e
addedValues at the north poled4e76d4f2628
addedParity of spherical harmonics1777c838d5d7
addedRotation transformation of spherical harmonics96bd82c1c0ab
addedH_ℓ as irreducible representation of SO(3)bc4f9d8ebb41
addedSpherical harmonic expansion (completeness)4eaf65e1e176
addedUniform convergence under rapid decayd092ed15575f
addedReal harmonic expansioncd9c84e427d8
addedCompleteness relationc0bbd84abb02
addedParseval-type theorem for spherical harmonicsbdea7c6cadb8
addedAngular power spectrum8d5948baf7c6
addedCross-power spectrum55c5d885d905
addedBest approximation error by spherical polynomialsda4d40879ffb
addedSobolev norm via spherical harmonic coefficients70131e999647
addedTruncation gives best L^2 approximationb370901b8a12
addedDecay implies Sobolev membership1c65084c7209
addedAddition theorem for spherical harmonicsb88028865942
addedUnsöld's theorem687d0a180adc
addedZonal harmonic decomposition in higher dimensions6b1cccb67dc5
addedZonal harmonic as Gegenbauer polynomial74c26217b36b
addedContraction rule for productsc45b9f8be01f
addedClebsch–Gordan coefficients40b72eaa5468
addedNodal lines of spherical harmonics289de0e7ffcc
addedZonal, sectoral, tesseral harmonics1c03aab7f872
addedHigher-dimensional spherical harmonicsf055cec0f41e
addedSolid spherical harmonics in n dimensions59f65b1c2045
addedProperties of H_ℓ in higher dimensionsc41fa746df9f
addedInductive construction via separation of variablesfd2353247d3f
addedH_ℓ irreducible representation of SO(3)9565b9960c64
addedH_ℓ isomorphic to traceless symmetric tensorsbc5e5656a7bb
addedHigher-dimensional irreducible representationd03f9b83a793
addedHemispherical harmonicse5388fd81272