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Statements
𝑸
ν
μ
(
z
)
=
π
1
/
2
(
z
2
-
1
)
μ
/
2
2
μ
Γ
(
μ
+
1
2
)
Γ
(
ν
-
μ
+
1
)
∫
0
∞
(
sinh
t
)
2
μ
(
z
+
(
z
2
-
1
)
1
/
2
cosh
t
)
ν
+
μ
+
1
d
t
,
associated-Legendre-black-Q
𝜇
𝜈
𝑧
superscript
𝜋
1
2
superscript
superscript
𝑧
2
1
𝜇
2
superscript
2
𝜇
Euler-Gamma
𝜇
1
2
Euler-Gamma
𝜈
𝜇
1
superscript
subscript
0
superscript
𝑡
2
𝜇
superscript
𝑧
superscript
superscript
𝑧
2
1
1
2
𝑡
𝜈
𝜇
1
𝑡
{\displaystyle{\displaystyle\boldsymbol{Q}^{\mu}_{\nu}\left(z\right)=\frac{\pi%
^{1/2}\left(z^{2}-1\right)^{\mu/2}}{2^{\mu}\Gamma\left(\mu+\frac{1}{2}\right)%
\Gamma\left(\nu-\mu+1\right)}\*\int_{0}^{\infty}\frac{(\sinh t)^{2\mu}}{\left(%
z+(z^{2}-1)^{1/2}\cosh t\right)^{\nu+\mu+1}}\mathrm{d}t,}}
ℜ
(
ν
+
1
)
>
ℜ
μ
>
-
1
2
𝜈
1
𝜇
1
2
{\displaystyle{\displaystyle\Re(\nu+1)>\Re\mu>-\tfrac{1}{2}}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\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}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
cosh
z
𝑧
{\displaystyle{\displaystyle\cosh\NVar{z}}}
sinh
z
𝑧
{\displaystyle{\displaystyle\sinh\NVar{z}}}
∫
{\displaystyle{\displaystyle\int}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
z
𝑧
{\displaystyle{\displaystyle z}}
μ
𝜇
{\displaystyle{\displaystyle\mu}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
