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Statements
𝖰
ν
μ
(
x
)
=
1
2
Γ
(
ν
+
μ
+
1
)
(
e
-
μ
π
i
/
2
𝑸
ν
μ
(
x
+
i
0
)
+
e
μ
π
i
/
2
𝑸
ν
μ
(
x
-
i
0
)
)
,
Ferrers-Legendre-Q-first-kind
𝜇
𝜈
𝑥
1
2
Euler-Gamma
𝜈
𝜇
1
superscript
𝑒
𝜇
𝜋
𝑖
2
associated-Legendre-black-Q
𝜇
𝜈
𝑥
𝑖
0
superscript
𝑒
𝜇
𝜋
𝑖
2
associated-Legendre-black-Q
𝜇
𝜈
𝑥
𝑖
0
{\displaystyle{\displaystyle\mathsf{Q}^{\mu}_{\nu}\left(x\right)=\tfrac{1}{2}%
\Gamma\left(\nu+\mu+1\right)\left(e^{-\mu\pi i/2}\boldsymbol{Q}^{\mu}_{\nu}%
\left(x+i0\right)+e^{\mu\pi i/2}\boldsymbol{Q}^{\mu}_{\nu}\left(x-i0\right)%
\right),}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\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)}}
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}}}
x
𝑥
{\displaystyle{\displaystyle x}}
μ
𝜇
{\displaystyle{\displaystyle\mu}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
