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Statements
𝖯
ν
μ
(
cos
θ
)
=
2
1
/
2
(
sin
θ
)
μ
π
1
/
2
Γ
(
1
2
-
μ
)
∫
0
θ
cos
(
(
ν
+
1
2
)
t
)
(
cos
t
-
cos
θ
)
μ
+
(
1
/
2
)
d
t
,
Ferrers-Legendre-P-first-kind
𝜇
𝜈
𝜃
superscript
2
1
2
superscript
𝜃
𝜇
superscript
𝜋
1
2
Euler-Gamma
1
2
𝜇
superscript
subscript
0
𝜃
𝜈
1
2
𝑡
superscript
𝑡
𝜃
𝜇
1
2
𝑡
{\displaystyle{\displaystyle\mathsf{P}^{\mu}_{\nu}\left(\cos\theta\right)=%
\frac{2^{1/2}(\sin\theta)^{\mu}}{\pi^{1/2}\Gamma\left(\frac{1}{2}-\mu\right)}%
\int_{0}^{\theta}\frac{\cos\left(\left(\nu+\frac{1}{2}\right)t\right)}{(\cos t%
-\cos\theta)^{\mu+(1/2)}}\mathrm{d}t,}}
ℜ
μ
<
1
2
𝜇
1
2
{\displaystyle{\displaystyle\Re\mu<\tfrac{1}{2}}}
0
<
θ
<
π
0
𝜃
𝜋
{\displaystyle{\displaystyle 0<\theta<\pi}}
ℜ
μ
<
1
2
𝜇
1
2
{\displaystyle{\displaystyle\Re\mu<\tfrac{1}{2}}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
𝖯
ν
μ
(
x
)
Ferrers-Legendre-P-first-kind
𝜇
𝜈
𝑥
{\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}%
\right)}}
π
{\displaystyle{\displaystyle\pi}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
∫
{\displaystyle{\displaystyle\int}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
μ
𝜇
{\displaystyle{\displaystyle\mu}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
