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 2.8.E35 - MaRDI portal
Statements
W
n
,
3
(
u
,
ξ
)
=
|
ξ
|
1
/
2
J
ν
(
u
|
ξ
|
1
/
2
)
∑
s
=
0
n
-
1
A
s
(
ξ
)
u
2
s
-
|
ξ
|
J
ν
+
1
(
u
|
ξ
|
1
/
2
)
∑
s
=
0
n
-
2
B
s
(
ξ
)
u
2
s
+
1
+
|
ξ
|
1
/
2
env
J
ν
(
u
|
ξ
|
1
/
2
)
O
(
1
u
2
n
-
1
)
,
subscript
𝑊
𝑛
3
𝑢
𝜉
superscript
𝜉
1
2
Bessel-J
𝜈
𝑢
superscript
𝜉
1
2
superscript
subscript
𝑠
0
𝑛
1
subscript
𝐴
𝑠
𝜉
superscript
𝑢
2
𝑠
𝜉
Bessel-J
𝜈
1
𝑢
superscript
𝜉
1
2
superscript
subscript
𝑠
0
𝑛
2
subscript
𝐵
𝑠
𝜉
superscript
𝑢
2
𝑠
1
superscript
𝜉
1
2
envelope-Bessel-J
𝜈
𝑢
superscript
𝜉
1
2
Big-O
1
superscript
𝑢
2
𝑛
1
{\displaystyle{\displaystyle W_{n,3}(u,\xi)=|\xi|^{1/2}J_{\nu}\left(u|\xi|^{1/%
2}\right)\sum_{s=0}^{n-1}\frac{A_{s}(\xi)}{u^{2s}}-|\xi|J_{\nu+1}\left(u|\xi|^%
{1/2}\right)\sum_{s=0}^{n-2}\frac{B_{s}(\xi)}{u^{2s+1}}+|\xi|^{1/2}\mathrm{env%
}\mskip-2.0mu J_{\nu}\left(u|\xi|^{1/2}\right)O\left(\frac{1}{u^{2n-1}}\right)%
,}}
J
ν
(
z
)
Bessel-J
𝜈
𝑧
{\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
O
(
x
)
Big-O
𝑥
{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
env
J
ν
(
x
)
envelope-Bessel-J
𝜈
𝑥
{\displaystyle{\displaystyle\mathrm{env}\mskip-2.0mu J_{\NVar{\nu}}\left(\NVar%
{x}\right)}}
W
n
,
j
(
u
,
ξ
)
subscript
𝑊
𝑛
𝑗
𝑢
𝜉
{\displaystyle{\displaystyle W_{n,j}(u,\xi)}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
n
𝑛
{\displaystyle{\displaystyle n}}
A
s
(
ξ
)
subscript
𝐴
𝑠
𝜉
{\displaystyle{\displaystyle A_{s}(\xi)}}
B
s
(
ξ
)
subscript
𝐵
𝑠
𝜉
{\displaystyle{\displaystyle B_{s}(\xi)}}
u
𝑢
{\displaystyle{\displaystyle u}}
