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Statements
𝑸
ν
,
s
μ
(
z
)
=
e
-
s
μ
π
i
𝑸
ν
μ
(
z
)
-
π
i
sin
(
s
μ
π
)
sin
(
μ
π
)
Γ
(
ν
-
μ
+
1
)
P
ν
-
μ
(
z
)
,
associated-Legendre-black-Q
𝜇
𝜈
𝑠
𝑧
superscript
𝑒
𝑠
𝜇
𝜋
𝑖
associated-Legendre-black-Q
𝜇
𝜈
𝑧
𝜋
𝑖
𝑠
𝜇
𝜋
𝜇
𝜋
Euler-Gamma
𝜈
𝜇
1
Legendre-P-first-kind
𝜇
𝜈
𝑧
{\displaystyle{\displaystyle\boldsymbol{Q}^{\mu}_{\nu,s}\left(z\right)=e^{-s%
\mu\pi i}\boldsymbol{Q}^{\mu}_{\nu}\left(z\right)-\frac{\pi i\sin\left(s\mu\pi%
\right)}{\sin\left(\mu\pi\right)\Gamma\left(\nu-\mu+1\right)}P^{-\mu}_{\nu}%
\left(z\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}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
z
𝑧
{\displaystyle{\displaystyle z}}
μ
𝜇
{\displaystyle{\displaystyle\mu}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
s
𝑠
{\displaystyle{\displaystyle s}}
