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Statements
2
Γ
(
ν
+
μ
+
1
)
Γ
(
μ
-
ν
)
𝖰
ν
μ
(
x
)
=
-
cos
(
ν
π
)
𝖯
ν
-
μ
(
x
)
+
cos
(
μ
π
)
𝖯
ν
-
μ
(
-
x
)
,
2
Euler-Gamma
𝜈
𝜇
1
Euler-Gamma
𝜇
𝜈
Ferrers-Legendre-Q-first-kind
𝜇
𝜈
𝑥
𝜈
𝜋
Ferrers-Legendre-P-first-kind
𝜇
𝜈
𝑥
𝜇
𝜋
Ferrers-Legendre-P-first-kind
𝜇
𝜈
𝑥
{\displaystyle{\displaystyle\frac{2}{\Gamma\left(\nu+\mu+1\right)\Gamma\left(%
\mu-\nu\right)}\mathsf{Q}^{\mu}_{\nu}\left(x\right)=-\cos\left(\nu\pi\right)%
\mathsf{P}^{-\mu}_{\nu}\left(x\right)+\cos\left(\mu\pi\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)}}
𝖰
ν
μ
(
x
)
Ferrers-Legendre-Q-first-kind
𝜇
𝜈
𝑥
{\displaystyle{\displaystyle\mathsf{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}%
\right)}}
π
{\displaystyle{\displaystyle\pi}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
x
𝑥
{\displaystyle{\displaystyle x}}
μ
𝜇
{\displaystyle{\displaystyle\mu}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
