球面調和関数表
Y 4 − 4 ( x ) = 3 16 35 2 π ⋅ e − 4 i φ ⋅ sin 4  θ {\displaystyle Y_{4}^{-4}(x)={\frac {3}{16}}{\sqrt {\frac {35}{2\pi }}}\cdot e^{-4i\varphi }\cdot \sin ^{4}\theta }
Y 4 − 3 ( x ) = 3 8 35 π ⋅ e − 3 i φ ⋅ sin 3  θ ⋅ cos  θ {\displaystyle Y_{4}^{-3}(x)={\frac {3}{8}}{\sqrt {\frac {35}{\pi }}}\cdot e^{-3i\varphi }\cdot \sin ^{3}\theta \cdot \cos \theta }
Y 4 − 2 ( x ) = 3 8 5 2 π ⋅ e − 2 i φ ⋅ sin 2  θ ⋅ ( 7 cos 2  θ − 1 ) {\displaystyle Y_{4}^{-2}(x)={\frac {3}{8}}{\sqrt {\frac {5}{2\pi }}}\cdot e^{-2i\varphi }\cdot \sin ^{2}\theta \cdot (7\cos ^{2}\theta -1)}
Y 10 0 ( x ) = 1 512 21 π ⋅ ( 46189 cos 10  θ − 109395 cos 8  θ + 90090 cos 6  θ − 30030 cos 4  θ + 3465 cos 2  θ − 63 ) {\displaystyle Y_{10}^{0}(x)={\frac {1}{512}}{\sqrt {\frac {21}{\pi }}}\cdot (46189\cos ^{10}\theta -109395\cos ^{8}\theta +90090\cos ^{6}\theta -30030\cos ^{4}\theta +3465\cos ^{2}\theta -63)}
Y 10 1 ( x ) = − 1 256 1155 2 π ⋅ e i φ ⋅ sin  θ ⋅ ( 4199 cos 9  θ − 7956 cos 7  θ + 4914 cos 5  θ − 1092 cos 3  θ + 63 cos  θ ) {\displaystyle Y_{10}^{1}(x)=-{\frac {1}{256}}{\sqrt {\frac {1155}{2\pi }}}\cdot e^{i\varphi }\cdot \sin \theta \cdot (4199\cos ^{9}\theta -7956\cos ^{7}\theta +4914\cos ^{5}\theta -1092\cos ^{3}\theta +63\cos \theta )}
Y 10 2 ( x ) = 3 512 385 2 π ⋅ e 2 i φ ⋅ sin 2  θ ⋅ ( 4199 cos 8  θ − 6188 cos 6  θ + 2730 cos 4  θ − 364 cos 2  θ + 7 ) {\displaystyle Y_{10}^{2}(x)={\frac {3}{512}}{\sqrt {\frac {385}{2\pi }}}\cdot e^{2i\varphi }\cdot \sin ^{2}\theta \cdot (4199\cos ^{8}\theta -6188\cos ^{6}\theta +2730\cos ^{4}\theta -364\cos ^{2}\theta +7)}
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 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)}