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Statements
𝑸
ν
μ
(
x
)
=
1
β
Γ
(
ν
+
μ
+
1
)
(
α
2
-
y
x
2
-
1
+
α
2
)
1
/
4
K
μ
(
(
ν
+
1
2
)
|
y
|
1
/
2
)
(
1
+
O
(
1
ν
)
)
,
associated-Legendre-black-Q
𝜇
𝜈
𝑥
1
𝛽
Euler-Gamma
𝜈
𝜇
1
superscript
superscript
𝛼
2
𝑦
superscript
𝑥
2
1
superscript
𝛼
2
1
4
modified-Bessel-second-kind
𝜇
𝜈
1
2
superscript
𝑦
1
2
1
Big-O
1
𝜈
{\displaystyle{\displaystyle\boldsymbol{Q}^{\mu}_{\nu}\left(x\right)=\frac{1}{%
\beta\Gamma\left(\nu+\mu+1\right)}\left(\frac{\alpha^{2}-y}{x^{2}-1+\alpha^{2}%
}\right)^{1/4}\*K_{\mu}\left(\left(\nu+\tfrac{1}{2}\right)|y|^{1/2}\right)%
\left(1+O\left(\frac{1}{\nu}\right)\right),}}
O
(
x
)
Big-O
𝑥
{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
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)}}
K
ν
(
z
)
modified-Bessel-second-kind
𝜈
𝑧
{\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}
x
𝑥
{\displaystyle{\displaystyle x}}
μ
𝜇
{\displaystyle{\displaystyle\mu}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
β
𝛽
{\displaystyle{\displaystyle\beta}}
y
𝑦
{\displaystyle{\displaystyle y}}
α
𝛼
{\displaystyle{\displaystyle\alpha}}
Identifiers
