球面調和関数表
Y 8 − 8 ( x ) = 3 256 12155 2 π ⋅ e − 8 i φ ⋅ sin 8  θ {\displaystyle Y_{8}^{-8}(x)={\frac {3}{256}}{\sqrt {\frac {12155}{2\pi }}}\cdot e^{-8i\varphi }\cdot \sin ^{8}\theta }
Y 8 − 7 ( x ) = 3 64 12155 2 π ⋅ e − 7 i φ ⋅ sin 7  θ ⋅ cos  θ {\displaystyle Y_{8}^{-7}(x)={\frac {3}{64}}{\sqrt {\frac {12155}{2\pi }}}\cdot e^{-7i\varphi }\cdot \sin ^{7}\theta \cdot \cos \theta }
Y 8 − 6 ( x ) = 1 128 7293 π ⋅ e − 6 i φ ⋅ sin 6  θ ⋅ ( 15 cos 2  θ − 1 ) {\displaystyle Y_{8}^{-6}(x)={\frac {1}{128}}{\sqrt {\frac {7293}{\pi }}}\cdot e^{-6i\varphi }\cdot \sin ^{6}\theta \cdot (15\cos ^{2}\theta -1)}
Y 4 , − 2 = g z 2 x y = i 1 2 ( Y 4 − 2 − Y 4 2 ) = 3 4 5 π ⋅ x y ⋅ ( 7 z 2 − r 2 ) r 4 {\displaystyle Y_{4,-2}=g_{z^{2}xy}=i{\sqrt {\frac {1}{2}}}\left(Y_{4}^{-2}-Y_{4}^{2}\right)={\frac {3}{4}}{\sqrt {\frac {5}{\pi }}}\cdot {\frac {xy\cdot (7z^{2}-r^{2})}{r^{4}}}}
Y 4 , − 1 = g z 3 y = i 1 2 ( Y 4 − 1 + Y 4 1 ) = 3 4 5 2 π ⋅ y z ⋅ ( 7 z 2 − 3 r 2 ) r 4 {\displaystyle Y_{4,-1}=g_{z^{3}y}=i{\sqrt {\frac {1}{2}}}\left(Y_{4}^{-1}+Y_{4}^{1}\right)={\frac {3}{4}}{\sqrt {\frac {5}{2\pi }}}\cdot {\frac {yz\cdot (7z^{2}-3r^{2})}{r^{4}}}}
Y 40 = g z 4 = Y 4 0 = 3 16 1 π ⋅ ( 35 z 4 − 30 z 2 r 2 + 3 r 4 ) r 4 {\displaystyle Y_{40}=g_{z^{4}}=Y_{4}^{0}={\frac {3}{16}}{\sqrt {\frac {1}{\pi }}}\cdot {\frac {(35z^{4}-30z^{2}r^{2}+3r^{4})}{r^{4}}}}
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 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 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 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 − 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 6 3 ( x ) = − 1 32 1365 π ⋅ e 3 i φ ⋅ sin 3  θ ⋅ ( 11 cos 3  θ − 3 cos  θ ) {\displaystyle Y_{6}^{3}(x)=-{\frac {1}{32}}{\sqrt {\frac {1365}{\pi }}}\cdot e^{3i\varphi }\cdot \sin ^{3}\theta \cdot (11\cos ^{3}\theta -3\cos \theta )}
Y 6 4 ( x ) = 3 32 91 2 π ⋅ e 4 i φ ⋅ sin 4  θ ⋅ ( 11 cos 2  θ − 1 ) {\displaystyle Y_{6}^{4}(x)={\frac {3}{32}}{\sqrt {\frac {91}{2\pi }}}\cdot e^{4i\varphi }\cdot \sin ^{4}\theta \cdot (11\cos ^{2}\theta -1)}
Y 6 5 ( x ) = − 3 32 1001 π ⋅ e 5 i φ ⋅ sin 5  θ ⋅ cos  θ {\displaystyle Y_{6}^{5}(x)=-{\frac {3}{32}}{\sqrt {\frac {1001}{\pi }}}\cdot e^{5i\varphi }\cdot \sin ^{5}\theta \cdot \cos \theta }
Y 6 6 ( x ) = 1 64 3003 π ⋅ e 6 i φ ⋅ sin 6  θ {\displaystyle Y_{6}^{6}(x)={\frac {1}{64}}{\sqrt {\frac {3003}{\pi }}}\cdot e^{6i\varphi }\cdot \sin ^{6}\theta }