Deprecated : $wgMWOAuthSharedUserIDs=false is deprecated, set $wgMWOAuthSharedUserIDs=true, $wgMWOAuthSharedUserSource='local' instead [Called from MediaWiki\HookContainer\HookContainer::run in /var/www/html/w/includes/HookContainer/HookContainer.php at line 135] in /var/www/html/w/includes/Debug/MWDebug.php on line 372 DLMF:14.20.E16 - MaRDI portal
Statements
𝖰
^
-
1
2
+
i
τ
-
μ
(
cos
θ
)
=
1
τ
μ
(
θ
sin
θ
)
1
/
2
K
μ
(
τ
θ
)
(
1
+
O
(
1
/
τ
)
)
,
Ferrers-conical-legendre-Q-hat
𝜇
1
2
𝑖
𝜏
𝜃
1
superscript
𝜏
𝜇
superscript
𝜃
𝜃
1
2
modified-Bessel-second-kind
𝜇
𝜏
𝜃
1
Big-O
1
𝜏
{\displaystyle{\displaystyle\widehat{\mathsf{Q}}^{-\mu}_{-\frac{1}{2}+i\tau}%
\left(\cos\theta\right)=\frac{1}{\tau^{\mu}}\left(\frac{\theta}{\sin\theta}%
\right)^{1/2}K_{\mu}\left(\tau\theta\right)\*\left(1+O\left(\ifrac{1}{\tau}%
\right)\right),}}
O
(
x
)
Big-O
𝑥
{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
𝖰
^
-
1
2
+
i
τ
-
μ
(
x
)
Ferrers-conical-legendre-Q-hat
𝜇
1
2
𝑖
𝜏
𝑥
{\displaystyle{\displaystyle\widehat{\mathsf{Q}}^{-\NVar{\mu}}_{\NVar{-\frac{1%
}{2}+i\tau}}\left(\NVar{x}\right)}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
K
ν
(
z
)
modified-Bessel-second-kind
𝜈
𝑧
{\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
τ
𝜏
{\displaystyle{\displaystyle\tau}}
μ
𝜇
{\displaystyle{\displaystyle\mu}}
0
<
θ
<
π
0
𝜃
𝜋
{\displaystyle{\displaystyle 0<\theta<\pi}}
