球面調和関数表
Y 9 − 1 ( x ) = 3 256 95 2 π ⋅ e − i φ ⋅ sin  θ ⋅ ( 2431 cos 8  θ − 4004 cos 6  θ + 2002 cos 4  θ − 308 cos 2  θ + 7 ) {\displaystyle Y_{9}^{-1}(x)={\frac {3}{256}}{\sqrt {\frac {95}{2\pi }}}\cdot e^{-i\varphi }\cdot \sin \theta \cdot (2431\cos ^{8}\theta -4004\cos ^{6}\theta +2002\cos ^{4}\theta -308\cos ^{2}\theta +7)}
Y 9 0 ( x ) = 1 256 19 π ⋅ ( 12155 cos 9  θ − 25740 cos 7  θ + 18018 cos 5  θ − 4620 cos 3  θ + 315 cos  θ ) {\displaystyle Y_{9}^{0}(x)={\frac {1}{256}}{\sqrt {\frac {19}{\pi }}}\cdot (12155\cos ^{9}\theta -25740\cos ^{7}\theta +18018\cos ^{5}\theta -4620\cos ^{3}\theta +315\cos \theta )}
Y 9 1 ( x ) = − 3 256 95 2 π ⋅ e i φ ⋅ sin  θ ⋅ ( 2431 cos 8  θ − 4004 cos 6  θ + 2002 cos 4  θ − 308 cos 2  θ + 7 ) {\displaystyle Y_{9}^{1}(x)=-{\frac {3}{256}}{\sqrt {\frac {95}{2\pi }}}\cdot e^{i\varphi }\cdot \sin \theta \cdot (2431\cos ^{8}\theta -4004\cos ^{6}\theta +2002\cos ^{4}\theta -308\cos ^{2}\theta +7)}
Y 9 − 9 ( x ) = 1 512 230945 π ⋅ e − 9 i φ ⋅ sin 9  θ {\displaystyle Y_{9}^{-9}(x)={\frac {1}{512}}{\sqrt {\frac {230945}{\pi }}}\cdot e^{-9i\varphi }\cdot \sin ^{9}\theta }
Y 9 − 8 ( x ) = 3 256 230945 2 π ⋅ e − 8 i φ ⋅ sin 8  θ ⋅ cos  θ {\displaystyle Y_{9}^{-8}(x)={\frac {3}{256}}{\sqrt {\frac {230945}{2\pi }}}\cdot e^{-8i\varphi }\cdot \sin ^{8}\theta \cdot \cos \theta }
Y 9 − 7 ( x ) = 3 512 13585 π ⋅ e − 7 i φ ⋅ sin 7  θ ⋅ ( 17 cos 2  θ − 1 ) {\displaystyle Y_{9}^{-7}(x)={\frac {3}{512}}{\sqrt {\frac {13585}{\pi }}}\cdot e^{-7i\varphi }\cdot \sin ^{7}\theta \cdot (17\cos ^{2}\theta -1)}
Y 9 7 ( x ) = − 3 512 13585 π ⋅ e 7 i φ ⋅ sin 7  θ ⋅ ( 17 cos 2  θ − 1 ) {\displaystyle Y_{9}^{7}(x)=-{\frac {3}{512}}{\sqrt {\frac {13585}{\pi }}}\cdot e^{7i\varphi }\cdot \sin ^{7}\theta \cdot (17\cos ^{2}\theta -1)}
Y 9 8 ( x ) = 3 256 230945 2 π ⋅ e 8 i φ ⋅ sin 8  θ ⋅ cos  θ {\displaystyle Y_{9}^{8}(x)={\frac {3}{256}}{\sqrt {\frac {230945}{2\pi }}}\cdot e^{8i\varphi }\cdot \sin ^{8}\theta \cdot \cos \theta }
Y 9 9 ( x ) = − 1 512 230945 π ⋅ e 9 i φ ⋅ sin 9  θ {\displaystyle Y_{9}^{9}(x)=-{\frac {1}{512}}{\sqrt {\frac {230945}{\pi }}}\cdot e^{9i\varphi }\cdot \sin ^{9}\theta }
Y 1 − 1 ( x ) = 1 2 3 2 π ⋅ e − i φ ⋅ sin  θ = 1 2 3 2 π ⋅ x − i y r {\displaystyle Y_{1}^{-1}(x)={\frac {1}{2}}{\sqrt {\frac {3}{2\pi }}}\cdot e^{-i\varphi }\cdot \sin \theta ={\frac {1}{2}}{\sqrt {\frac {3}{2\pi }}}\cdot {\frac {x-iy}{r}}}
Y 1 0 ( x ) = 1 2 3 π ⋅ cos  θ = 1 2 3 π ⋅ z r {\displaystyle Y_{1}^{0}(x)={\frac {1}{2}}{\sqrt {\frac {3}{\pi }}}\cdot \cos \theta ={\frac {1}{2}}{\sqrt {\frac {3}{\pi }}}\cdot {\frac {z}{r}}}
Y 1 1 ( x ) = − 1 2 3 2 π ⋅ e i φ ⋅ sin  θ = − 1 2 3 2 π ⋅ x + i y r {\displaystyle Y_{1}^{1}(x)=-{\frac {1}{2}}{\sqrt {\frac {3}{2\pi }}}\cdot e^{i\varphi }\cdot \sin \theta =-{\frac {1}{2}}{\sqrt {\frac {3}{2\pi }}}\cdot {\frac {x+iy}{r}}}
Y 1 , − 1 = p y = i 1 2 ( Y 1 − 1 + Y 1 1 ) = 3 4 π ⋅ y r {\displaystyle Y_{1,-1}=p_{y}=i{\sqrt {\frac {1}{2}}}\left(Y_{1}^{-1}+Y_{1}^{1}\right)={\sqrt {\frac {3}{4\pi }}}\cdot {\frac {y}{r}}}
Y 10 = p z = Y 1 0 = 3 4 π ⋅ z r {\displaystyle Y_{10}=p_{z}=Y_{1}^{0}={\sqrt {\frac {3}{4\pi }}}\cdot {\frac {z}{r}}}
Y 11 = p x = 1 2 ( Y 1 − 1 − Y 1 1 ) = 3 4 π ⋅ x r {\displaystyle Y_{11}=p_{x}={\sqrt {\frac {1}{2}}}\left(Y_{1}^{-1}-Y_{1}^{1}\right)={\sqrt {\frac {3}{4\pi }}}\cdot {\frac {x}{r}}}