球面調和関数表
Y 8 3 ( x ) = − 1 64 19635 2 π ⋅ e 3 i φ ⋅ sin 3  θ ⋅ ( 39 cos 5  θ − 26 cos 3  θ + 3 cos  θ ) {\displaystyle Y_{8}^{3}(x)=-{\frac {1}{64}}{\sqrt {\frac {19635}{2\pi }}}\cdot e^{3i\varphi }\cdot \sin ^{3}\theta \cdot (39\cos ^{5}\theta -26\cos ^{3}\theta +3\cos \theta )}
Y 8 4 ( x ) = 3 128 1309 2 π ⋅ e 4 i φ ⋅ sin 4  θ ⋅ ( 65 cos 4  θ − 26 cos 2  θ + 1 ) {\displaystyle Y_{8}^{4}(x)={\frac {3}{128}}{\sqrt {\frac {1309}{2\pi }}}\cdot e^{4i\varphi }\cdot \sin ^{4}\theta \cdot (65\cos ^{4}\theta -26\cos ^{2}\theta +1)}
Y 8 5 ( x ) = − 3 64 17017 2 π ⋅ e 5 i φ ⋅ sin 5  θ ⋅ ( 5 cos 3  θ − 1 cos  θ ) {\displaystyle Y_{8}^{5}(x)=-{\frac {3}{64}}{\sqrt {\frac {17017}{2\pi }}}\cdot e^{5i\varphi }\cdot \sin ^{5}\theta \cdot (5\cos ^{3}\theta -1\cos \theta )}
Y 10 − 4 ( x ) = 3 256 5005 2 π ⋅ e − 4 i φ ⋅ sin 4  θ ⋅ ( 323 cos 6  θ − 255 cos 4  θ + 45 cos 2  θ − 1 ) {\displaystyle Y_{10}^{-4}(x)={\frac {3}{256}}{\sqrt {\frac {5005}{2\pi }}}\cdot e^{-4i\varphi }\cdot \sin ^{4}\theta \cdot (323\cos ^{6}\theta -255\cos ^{4}\theta +45\cos ^{2}\theta -1)}
Y 10 − 3 ( x ) = 3 256 5005 π ⋅ e − 3 i φ ⋅ sin 3  θ ⋅ ( 323 cos 7  θ − 357 cos 5  θ + 105 cos 3  θ − 7 cos  θ ) {\displaystyle Y_{10}^{-3}(x)={\frac {3}{256}}{\sqrt {\frac {5005}{\pi }}}\cdot e^{-3i\varphi }\cdot \sin ^{3}\theta \cdot (323\cos ^{7}\theta -357\cos ^{5}\theta +105\cos ^{3}\theta -7\cos \theta )}
Y 9 − 3 ( x ) = 1 256 21945 π ⋅ e − 3 i φ ⋅ sin 3  θ ⋅ ( 221 cos 6  θ − 195 cos 4  θ + 39 cos 2  θ − 1 ) {\displaystyle Y_{9}^{-3}(x)={\frac {1}{256}}{\sqrt {\frac {21945}{\pi }}}\cdot e^{-3i\varphi }\cdot \sin ^{3}\theta \cdot (221\cos ^{6}\theta -195\cos ^{4}\theta +39\cos ^{2}\theta -1)}
Y 9 − 2 ( x ) = 3 128 1045 π ⋅ e − 2 i φ ⋅ sin 2  θ ⋅ ( 221 cos 7  θ − 273 cos 5  θ + 91 cos 3  θ − 7 cos  θ ) {\displaystyle Y_{9}^{-2}(x)={\frac {3}{128}}{\sqrt {\frac {1045}{\pi }}}\cdot e^{-2i\varphi }\cdot \sin ^{2}\theta \cdot (221\cos ^{7}\theta -273\cos ^{5}\theta +91\cos ^{3}\theta -7\cos \theta )}
Y 10 8 ( x ) = 1 512 255255 2 π ⋅ e 8 i φ ⋅ sin 8  θ ⋅ ( 19 cos 2  θ − 1 ) {\displaystyle Y_{10}^{8}(x)={\frac {1}{512}}{\sqrt {\frac {255255}{2\pi }}}\cdot e^{8i\varphi }\cdot \sin ^{8}\theta \cdot (19\cos ^{2}\theta -1)}
Y 10 9 ( x ) = − 1 512 4849845 π ⋅ e 9 i φ ⋅ sin 9  θ ⋅ cos  θ {\displaystyle Y_{10}^{9}(x)=-{\frac {1}{512}}{\sqrt {\frac {4849845}{\pi }}}\cdot e^{9i\varphi }\cdot \sin ^{9}\theta \cdot \cos \theta }
Y 10 10 ( x ) = 1 1024 969969 π ⋅ e 10 i φ ⋅ sin 10  θ {\displaystyle Y_{10}^{10}(x)={\frac {1}{1024}}{\sqrt {\frac {969969}{\pi }}}\cdot e^{10i\varphi }\cdot \sin ^{10}\theta }
Y 8 0 ( x ) = 1 256 17 π ⋅ ( 6435 cos 8  θ − 12012 cos 6  θ + 6930 cos 4  θ − 1260 cos 2  θ + 35 ) {\displaystyle Y_{8}^{0}(x)={\frac {1}{256}}{\sqrt {\frac {17}{\pi }}}\cdot (6435\cos ^{8}\theta -12012\cos ^{6}\theta +6930\cos ^{4}\theta -1260\cos ^{2}\theta +35)}
Y 8 1 ( x ) = − 3 64 17 2 π ⋅ e i φ ⋅ sin  θ ⋅ ( 715 cos 7  θ − 1001 cos 5  θ + 385 cos 3  θ − 35 cos  θ ) {\displaystyle Y_{8}^{1}(x)=-{\frac {3}{64}}{\sqrt {\frac {17}{2\pi }}}\cdot e^{i\varphi }\cdot \sin \theta \cdot (715\cos ^{7}\theta -1001\cos ^{5}\theta +385\cos ^{3}\theta -35\cos \theta )}
Y 8 2 ( x ) = 3 128 595 π ⋅ e 2 i φ ⋅ sin 2  θ ⋅ ( 143 cos 6  θ − 143 cos 4  θ + 33 cos 2  θ − 1 ) {\displaystyle Y_{8}^{2}(x)={\frac {3}{128}}{\sqrt {\frac {595}{\pi }}}\cdot e^{2i\varphi }\cdot \sin ^{2}\theta \cdot (143\cos ^{6}\theta -143\cos ^{4}\theta +33\cos ^{2}\theta -1)}
Y 5 0 ( x ) = 1 16 11 π ⋅ ( 63 cos 5  θ − 70 cos 3  θ + 15 cos  θ ) {\displaystyle Y_{5}^{0}(x)={\frac {1}{16}}{\sqrt {\frac {11}{\pi }}}\cdot (63\cos ^{5}\theta -70\cos ^{3}\theta +15\cos \theta )}
Y 5 1 ( x ) = − 1 16 165 2 π ⋅ e i φ ⋅ sin  θ ⋅ ( 21 cos 4  θ − 14 cos 2  θ + 1 ) {\displaystyle Y_{5}^{1}(x)=-{\frac {1}{16}}{\sqrt {\frac {165}{2\pi }}}\cdot e^{i\varphi }\cdot \sin \theta \cdot (21\cos ^{4}\theta -14\cos ^{2}\theta +1)}
Y 5 2 ( x ) = 1 8 1155 2 π ⋅ e 2 i φ ⋅ sin 2  θ ⋅ ( 3 cos 3  θ − 1 cos  θ ) {\displaystyle Y_{5}^{2}(x)={\frac {1}{8}}{\sqrt {\frac {1155}{2\pi }}}\cdot e^{2i\varphi }\cdot \sin ^{2}\theta \cdot (3\cos ^{3}\theta -1\cos \theta )}