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Statements
𝖰
ν
μ
(
x
)
∼
(
-
1
)
μ
+
(
1
/
2
)
π
Γ
(
ν
+
μ
+
1
)
2
Γ
(
μ
+
1
)
Γ
(
ν
-
μ
+
1
)
(
1
-
x
2
)
μ
/
2
,
asymptotically-equals
Ferrers-Legendre-Q-first-kind
𝜇
𝜈
𝑥
superscript
1
𝜇
1
2
𝜋
Euler-Gamma
𝜈
𝜇
1
2
Euler-Gamma
𝜇
1
Euler-Gamma
𝜈
𝜇
1
superscript
1
𝑥
2
𝜇
2
{\displaystyle{\displaystyle\mathsf{Q}^{\mu}_{\nu}\left(x\right)\sim(-1)^{\mu+%
(1/2)}\frac{\pi\Gamma\left(\nu+\mu+1\right)}{2\Gamma\left(\mu+1\right)\Gamma%
\left(\nu-\mu+1\right)}\left(\frac{1-x}{2}\right)^{\mu/2},}}
ν
±
μ
≠
-
1
,
-
2
,
-
3
,
…
plus-or-minus
𝜈
𝜇
1
2
3
…
{\displaystyle{\displaystyle\nu\pm\mu\neq-1,-2,-3,\dots}}
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)}}
∼
asymptotically-equals
{\displaystyle{\displaystyle\sim}}
π
{\displaystyle{\displaystyle\pi}}
x
𝑥
{\displaystyle{\displaystyle x}}
μ
𝜇
{\displaystyle{\displaystyle\mu}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
