球面調和関数表
Y 6 − 2 ( x ) = 1 64 1365 π ⋅ e − 2 i φ ⋅ sin 2  θ ⋅ ( 33 cos 4  θ − 18 cos 2  θ + 1 ) {\displaystyle Y_{6}^{-2}(x)={\frac {1}{64}}{\sqrt {\frac {1365}{\pi }}}\cdot e^{-2i\varphi }\cdot \sin ^{2}\theta \cdot (33\cos ^{4}\theta -18\cos ^{2}\theta +1)}
Y 6 − 1 ( x ) = 1 16 273 2 π ⋅ e − i φ ⋅ sin  θ ⋅ ( 33 cos 5  θ − 30 cos 3  θ + 5 cos  θ ) {\displaystyle Y_{6}^{-1}(x)={\frac {1}{16}}{\sqrt {\frac {273}{2\pi }}}\cdot e^{-i\varphi }\cdot \sin \theta \cdot (33\cos ^{5}\theta -30\cos ^{3}\theta +5\cos \theta )}
Y 7 4 ( x ) = 3 32 385 2 π ⋅ e 4 i φ ⋅ sin 4  θ ⋅ ( 13 cos 3  θ − 3 cos  θ ) {\displaystyle Y_{7}^{4}(x)={\frac {3}{32}}{\sqrt {\frac {385}{2\pi }}}\cdot e^{4i\varphi }\cdot \sin ^{4}\theta \cdot (13\cos ^{3}\theta -3\cos \theta )}
Y 7 5 ( x ) = − 3 64 385 2 π ⋅ e 5 i φ ⋅ sin 5  θ ⋅ ( 13 cos 2  θ − 1 ) {\displaystyle Y_{7}^{5}(x)=-{\frac {3}{64}}{\sqrt {\frac {385}{2\pi }}}\cdot e^{5i\varphi }\cdot \sin ^{5}\theta \cdot (13\cos ^{2}\theta -1)}
Y 7 6 ( x ) = 3 64 5005 π ⋅ e 6 i φ ⋅ sin 6  θ ⋅ cos  θ {\displaystyle Y_{7}^{6}(x)={\frac {3}{64}}{\sqrt {\frac {5005}{\pi }}}\cdot e^{6i\varphi }\cdot \sin ^{6}\theta \cdot \cos \theta }
Y 7 7 ( x ) = − 3 64 715 2 π ⋅ e 7 i φ ⋅ sin 7  θ {\displaystyle Y_{7}^{7}(x)=-{\frac {3}{64}}{\sqrt {\frac {715}{2\pi }}}\cdot e^{7i\varphi }\cdot \sin ^{7}\theta }
Y 5 3 ( x ) = − 1 32 385 π ⋅ e 3 i φ ⋅ sin 3  θ ⋅ ( 9 cos 2  θ − 1 ) {\displaystyle Y_{5}^{3}(x)=-{\frac {1}{32}}{\sqrt {\frac {385}{\pi }}}\cdot e^{3i\varphi }\cdot \sin ^{3}\theta \cdot (9\cos ^{2}\theta -1)}
Y 5 4 ( x ) = 3 16 385 2 π ⋅ e 4 i φ ⋅ sin 4  θ ⋅ cos  θ {\displaystyle Y_{5}^{4}(x)={\frac {3}{16}}{\sqrt {\frac {385}{2\pi }}}\cdot e^{4i\varphi }\cdot \sin ^{4}\theta \cdot \cos \theta }
Y 5 5 ( x ) = − 3 32 77 π ⋅ e 5 i φ ⋅ sin 5  θ {\displaystyle Y_{5}^{5}(x)=-{\frac {3}{32}}{\sqrt {\frac {77}{\pi }}}\cdot e^{5i\varphi }\cdot \sin ^{5}\theta }