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Statements
P
ν
(
z
1
z
2
-
(
z
1
2
-
1
)
1
/
2
(
z
2
2
-
1
)
1
/
2
cos
ϕ
)
=
P
ν
(
z
1
)
P
ν
(
z
2
)
+
2
∑
m
=
1
∞
(
-
1
)
m
Γ
(
ν
-
m
+
1
)
Γ
(
ν
+
m
+
1
)
P
ν
m
(
z
1
)
P
ν
m
(
z
2
)
cos
(
m
ϕ
)
,
shorthand-Legendre-P-first-kind
𝜈
subscript
𝑧
1
subscript
𝑧
2
superscript
superscript
subscript
𝑧
1
2
1
1
2
superscript
superscript
subscript
𝑧
2
2
1
1
2
italic-ϕ
shorthand-Legendre-P-first-kind
𝜈
subscript
𝑧
1
shorthand-Legendre-P-first-kind
𝜈
subscript
𝑧
2
2
superscript
subscript
𝑚
1
superscript
1
𝑚
Euler-Gamma
𝜈
𝑚
1
Euler-Gamma
𝜈
𝑚
1
Legendre-P-first-kind
𝑚
𝜈
subscript
𝑧
1
Legendre-P-first-kind
𝑚
𝜈
subscript
𝑧
2
𝑚
italic-ϕ
{\displaystyle{\displaystyle P_{\nu}\left(z_{1}z_{2}-\left(z_{1}^{2}-1\right)^%
{1/2}\left(z_{2}^{2}-1\right)^{1/2}\cos\phi\right)=P_{\nu}\left(z_{1}\right)P_%
{\nu}\left(z_{2}\right)+2\sum_{m=1}^{\infty}(-1)^{m}\frac{\Gamma\left(\nu-m+1%
\right)}{\Gamma\left(\nu+m+1\right)}\*P^{m}_{\nu}\left(z_{1}\right)P^{m}_{\nu}%
(z_{2})\cos\left(m\phi\right),}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
P
ν
μ
(
z
)
Legendre-P-first-kind
𝜇
𝜈
𝑧
{\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
P
ν
(
z
)
=
P
ν
0
(
z
)
shorthand-Legendre-P-first-kind
𝜈
𝑧
Legendre-P-first-kind
0
𝜈
𝑧
{\displaystyle{\displaystyle P_{\NVar{\nu}}\left(\NVar{z}\right)=P^{0}_{\nu}%
\left(z\right)}}
z
𝑧
{\displaystyle{\displaystyle z}}
m
𝑚
{\displaystyle{\displaystyle m}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
