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:11.6.E2 - MaRDI portal
Statements
𝐌
ν
(
z
)
∼
1
π
∑
k
=
0
∞
(
-
1
)
k
+
1
Γ
(
k
+
1
2
)
(
1
2
z
)
ν
-
2
k
-
1
Γ
(
ν
+
1
2
-
k
)
,
asymptotic-expansion
associated-Struve-M
𝜈
𝑧
1
𝜋
superscript
subscript
𝑘
0
superscript
1
𝑘
1
Euler-Gamma
𝑘
1
2
superscript
1
2
𝑧
𝜈
2
𝑘
1
Euler-Gamma
𝜈
1
2
𝑘
{\displaystyle{\displaystyle\mathbf{M}_{\nu}\left(z\right)\sim\frac{1}{\pi}%
\sum_{k=0}^{\infty}(-1)^{k+1}\frac{\Gamma\left(k+\tfrac{1}{2}\right)(\tfrac{1}%
{2}z)^{\nu-2k-1}}{\Gamma\left(\nu+\tfrac{1}{2}-k\right)},}}
|
ph
z
|
≤
1
2
π
-
δ
phase
𝑧
1
2
𝜋
𝛿
{\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{1}{2}\pi-\delta}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
𝐌
ν
(
z
)
associated-Struve-M
𝜈
𝑧
{\displaystyle{\displaystyle\mathbf{M}_{\NVar{\nu}}\left(\NVar{z}\right)}}
∼
asymptotic-expansion
{\displaystyle{\displaystyle\sim}}
π
{\displaystyle{\displaystyle\pi}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
k
𝑘
{\displaystyle{\displaystyle k}}
δ
𝛿
{\displaystyle{\displaystyle\delta}}
