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Statements
sin
(
(
ν
-
μ
)
π
)
Γ
(
ν
+
μ
+
1
)
𝖯
ν
μ
(
x
)
=
sin
(
ν
π
)
Γ
(
ν
-
μ
+
1
)
𝖯
ν
-
μ
(
x
)
-
sin
(
μ
π
)
Γ
(
ν
-
μ
+
1
)
𝖯
ν
-
μ
(
-
x
)
,
𝜈
𝜇
𝜋
Euler-Gamma
𝜈
𝜇
1
Ferrers-Legendre-P-first-kind
𝜇
𝜈
𝑥
𝜈
𝜋
Euler-Gamma
𝜈
𝜇
1
Ferrers-Legendre-P-first-kind
𝜇
𝜈
𝑥
𝜇
𝜋
Euler-Gamma
𝜈
𝜇
1
Ferrers-Legendre-P-first-kind
𝜇
𝜈
𝑥
{\displaystyle{\displaystyle\frac{\sin\left((\nu-\mu)\pi\right)}{\Gamma\left(%
\nu+\mu+1\right)}\mathsf{P}^{\mu}_{\nu}\left(x\right)=\frac{\sin\left(\nu\pi%
\right)}{\Gamma\left(\nu-\mu+1\right)}\mathsf{P}^{-\mu}_{\nu}\left(x\right)-%
\frac{\sin\left(\mu\pi\right)}{\Gamma\left(\nu-\mu+1\right)}\mathsf{P}^{-\mu}_%
{\nu}\left(-x\right),}}
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}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
x
𝑥
{\displaystyle{\displaystyle x}}
μ
𝜇
{\displaystyle{\displaystyle\mu}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
