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Statements
𝖰
ν
μ
(
x
)
=
e
∓
μ
π
i
/
2
Γ
(
ν
+
μ
+
1
)
𝑸
ν
μ
(
x
±
i
0
)
±
1
2
π
i
e
±
μ
π
i
/
2
P
ν
μ
(
x
±
i
0
)
.
Ferrers-Legendre-Q-first-kind
𝜇
𝜈
𝑥
plus-or-minus
superscript
𝑒
minus-or-plus
𝜇
𝜋
𝑖
2
Euler-Gamma
𝜈
𝜇
1
associated-Legendre-black-Q
𝜇
𝜈
plus-or-minus
𝑥
𝑖
0
1
2
𝜋
𝑖
superscript
𝑒
plus-or-minus
𝜇
𝜋
𝑖
2
Legendre-P-first-kind
𝜇
𝜈
plus-or-minus
𝑥
𝑖
0
{\displaystyle{\displaystyle\mathsf{Q}^{\mu}_{\nu}\left(x\right)=e^{\mp\mu\pi i%
/2}\Gamma\left(\nu+\mu+1\right)\boldsymbol{Q}^{\mu}_{\nu}\left(x\pm i0\right)%
\pm\tfrac{1}{2}\pi ie^{\pm\mu\pi i/2}P^{\mu}_{\nu}\left(x\pm i0\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)}}
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}}}
x
𝑥
{\displaystyle{\displaystyle x}}
μ
𝜇
{\displaystyle{\displaystyle\mu}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
