球面調和関数表
Y 00 = s = Y 0 0 = 1 2 1 π {\displaystyle Y_{00}=s=Y_{0}^{0}={\frac {1}{2}}{\sqrt {\frac {1}{\pi }}}}
l = 0 から l = 5 までは Varshalovich, Moskalev & Khersonskii (1988) を典拠としている。また、l = 0 から l = 3 までの θ 形式での関数は MathWorld でも確認できる。
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 )}
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 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 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 − 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)}