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Statements
δ
(
cos
θ
1
-
cos
θ
2
)
δ
(
ϕ
1
-
ϕ
2
)
=
∑
ℓ
=
0
∞
∑
m
=
-
ℓ
ℓ
Y
ℓ
,
m
(
θ
1
,
ϕ
1
)
Y
ℓ
,
m
(
θ
2
,
ϕ
2
)
¯
.
Dirac-delta
subscript
𝜃
1
subscript
𝜃
2
Dirac-delta
subscript
italic-ϕ
1
subscript
italic-ϕ
2
superscript
subscript
ℓ
0
superscript
subscript
𝑚
ℓ
ℓ
spherical-harmonic-Y
ℓ
𝑚
subscript
𝜃
1
subscript
italic-ϕ
1
spherical-harmonic-Y
ℓ
𝑚
subscript
𝜃
2
subscript
italic-ϕ
2
{\displaystyle{\displaystyle\delta\left(\cos\theta_{1}-\cos\theta_{2}\right)%
\delta\left(\phi_{1}-\phi_{2}\right)=\sum_{\ell=0}^{\infty}\sum_{m=-\ell}^{%
\ell}Y_{{\ell},{m}}\left(\theta_{1},\phi_{1}\right)\overline{Y_{{\ell},{m}}%
\left(\theta_{2},\phi_{2}\right)}.}}
δ
(
x
-
a
)
Dirac-delta
𝑥
𝑎
{\displaystyle{\displaystyle\delta\left(\NVar{x-a}\right)}}
z
¯
𝑧
{\displaystyle{\displaystyle\overline{\NVar{z}}}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
Y
l
,
m
(
θ
,
ϕ
)
spherical-harmonic-Y
𝑙
𝑚
𝜃
italic-ϕ
{\displaystyle{\displaystyle Y_{{\NVar{l}},{\NVar{m}}}\left(\NVar{\theta},%
\NVar{\phi}\right)}}
m
𝑚
{\displaystyle{\displaystyle m}}
Identifiers
