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In physics and mathematics, the solid harmonics are solutions of the Laplace equation in spherical polar coordinates, assumed to be (smooth) functions . There are two kinds: the regular solid harmonics , which are well-defined at the origin and the irregular solid harmonics , which are singular at the origin. Both sets of functions play an important role in potential theory, and are obtained by rescaling spherical harmonics appropriately:

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  • 体球調和関数 (ja)
  • Solid harmonics (en)
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  • In physics and mathematics, the solid harmonics are solutions of the Laplace equation in spherical polar coordinates, assumed to be (smooth) functions . There are two kinds: the regular solid harmonics , which are well-defined at the origin and the irregular solid harmonics , which are singular at the origin. Both sets of functions play an important role in potential theory, and are obtained by rescaling spherical harmonics appropriately: (en)
  • 物理学と数学において、体球調和関数(たいきゅうちょうわかんすう、英: solid harmonics)は球面座標系でのラプラス方程式の解を指す。原点で0になる正則な(regular)体球調和関数 と、原点が特異点となる非正則な(irregular)体球調和関数 の2種がある。いずれの関数集合もポテンシャル論で重要な役割を演じ、また適当にスケーリングすることで球面調和関数が得られる。 (ja)
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  • In physics and mathematics, the solid harmonics are solutions of the Laplace equation in spherical polar coordinates, assumed to be (smooth) functions . There are two kinds: the regular solid harmonics , which are well-defined at the origin and the irregular solid harmonics , which are singular at the origin. Both sets of functions play an important role in potential theory, and are obtained by rescaling spherical harmonics appropriately: (en)
  • 物理学と数学において、体球調和関数(たいきゅうちょうわかんすう、英: solid harmonics)は球面座標系でのラプラス方程式の解を指す。原点で0になる正則な(regular)体球調和関数 と、原点が特異点となる非正則な(irregular)体球調和関数 の2種がある。いずれの関数集合もポテンシャル論で重要な役割を演じ、また適当にスケーリングすることで球面調和関数が得られる。 (ja)
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