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Statements
𝖰
ν
-
μ
(
x
)
=
-
π
β
2
(
y
-
α
2
1
-
α
2
-
x
2
)
1
/
4
(
Y
μ
(
(
ν
+
1
2
)
y
1
/
2
)
+
O
(
1
ν
)
env
Y
μ
(
(
ν
+
1
2
)
y
1
/
2
)
)
,
Ferrers-Legendre-Q-first-kind
𝜇
𝜈
𝑥
𝜋
𝛽
2
superscript
𝑦
superscript
𝛼
2
1
superscript
𝛼
2
superscript
𝑥
2
1
4
Bessel-Y-Weber
𝜇
𝜈
1
2
superscript
𝑦
1
2
Big-O
1
𝜈
envelope-Bessel-Y
𝜇
𝜈
1
2
superscript
𝑦
1
2
{\displaystyle{\displaystyle\mathsf{Q}^{-\mu}_{\nu}\left(x\right)=-\frac{\pi%
\beta}{2}\left(\frac{y-\alpha^{2}}{1-\alpha^{2}-x^{2}}\right)^{1/4}\left(Y_{%
\mu}\left(\left(\nu+\tfrac{1}{2}\right)y^{1/2}\right)+O\left(\frac{1}{\nu}%
\right)\mathrm{env}\mskip-2.0mu Y_{\mu}\left(\left(\nu+\tfrac{1}{2}\right)y^{1%
/2}\right)\right),}}
Y
ν
(
z
)
Bessel-Y-Weber
𝜈
𝑧
{\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}
O
(
x
)
Big-O
𝑥
{\displaystyle{\displaystyle O\left(\NVar{x}\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)}}
π
{\displaystyle{\displaystyle\pi}}
env
Y
ν
(
x
)
envelope-Bessel-Y
𝜈
𝑥
{\displaystyle{\displaystyle\mathrm{env}\mskip-2.0mu Y_{\NVar{\nu}}\left(\NVar%
{x}\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}}
