球面調和関数表
Y 4 − 1 ( x ) = 3 8 5 π ⋅ e − i φ ⋅ sin  θ ⋅ ( 7 cos 3  θ − 3 cos  θ ) {\displaystyle Y_{4}^{-1}(x)={\frac {3}{8}}{\sqrt {\frac {5}{\pi }}}\cdot e^{-i\varphi }\cdot \sin \theta \cdot (7\cos ^{3}\theta -3\cos \theta )}
Y 4 0 ( x ) = 3 16 1 π ⋅ ( 35 cos 4  θ − 30 cos 2  θ + 3 ) {\displaystyle Y_{4}^{0}(x)={\frac {3}{16}}{\sqrt {\frac {1}{\pi }}}\cdot (35\cos ^{4}\theta -30\cos ^{2}\theta +3)}
Y 4 1 ( x ) = − 3 8 5 π ⋅ e i φ ⋅ sin  θ ⋅ ( 7 cos 3  θ − 3 cos  θ ) {\displaystyle Y_{4}^{1}(x)=-{\frac {3}{8}}{\sqrt {\frac {5}{\pi }}}\cdot e^{i\varphi }\cdot \sin \theta \cdot (7\cos ^{3}\theta -3\cos \theta )}
Y 0 0 ( x ) = 1 2 1 π {\displaystyle Y_{0}^{0}(x)={\frac {1}{2}}{\sqrt {\frac {1}{\pi }}}}
Y 43 = g z x 3 = 1 2 ( Y 4 − 3 − Y 4 3 ) = 3 4 35 2 π ⋅ ( x 2 − 3 y 2 ) x z r 4 {\displaystyle Y_{43}=g_{zx^{3}}={\sqrt {\frac {1}{2}}}\left(Y_{4}^{-3}-Y_{4}^{3}\right)={\frac {3}{4}}{\sqrt {\frac {35}{2\pi }}}\cdot {\frac {(x^{2}-3y^{2})xz}{r^{4}}}}
Y 44 = g x 4 + y 4 = 1 2 ( Y 4 − 4 + Y 4 4 ) = 3 16 35 π ⋅ x 2 ( x 2 − 3 y 2 ) − y 2 ( 3 x 2 − y 2 ) r 4 {\displaystyle Y_{44}=g_{x^{4}+y^{4}}={\sqrt {\frac {1}{2}}}\left(Y_{4}^{-4}+Y_{4}^{4}\right)={\frac {3}{16}}{\sqrt {\frac {35}{\pi }}}\cdot {\frac {x^{2}\left(x^{2}-3y^{2}\right)-y^{2}\left(3x^{2}-y^{2}\right)}{r^{4}}}}