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Statements
cos
(
ν
π
)
P
ν
-
μ
(
x
)
=
-
𝑸
ν
μ
(
x
)
Γ
(
μ
-
ν
)
+
𝑸
-
ν
-
1
μ
(
x
)
Γ
(
ν
+
μ
+
1
)
.
𝜈
𝜋
Legendre-P-first-kind
𝜇
𝜈
𝑥
associated-Legendre-black-Q
𝜇
𝜈
𝑥
Euler-Gamma
𝜇
𝜈
associated-Legendre-black-Q
𝜇
𝜈
1
𝑥
Euler-Gamma
𝜈
𝜇
1
{\displaystyle{\displaystyle\cos\left(\nu\pi\right)P^{-\mu}_{\nu}\left(x\right%
)=-\frac{\boldsymbol{Q}^{\mu}_{\nu}\left(x\right)}{\Gamma\left(\mu-\nu\right)}%
+\frac{\boldsymbol{Q}^{\mu}_{-\nu-1}\left(x\right)}{\Gamma\left(\nu+\mu+1%
\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)}}
𝑸
ν
μ
(
z
)
associated-Legendre-black-Q
𝜇
𝜈
𝑧
{\displaystyle{\displaystyle\boldsymbol{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(%
\NVar{z}\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}}
Identifiers
