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:10.22.E70 - MaRDI portal
Statements
∫
0
∞
Y
ν
(
a
t
)
J
ν
+
1
(
b
t
)
t
d
t
t
2
-
z
2
=
1
2
π
J
ν
+
1
(
b
z
)
H
ν
(
1
)
(
a
z
)
,
superscript
subscript
0
Bessel-Y-Weber
𝜈
𝑎
𝑡
Bessel-J
𝜈
1
𝑏
𝑡
𝑡
𝑡
superscript
𝑡
2
superscript
𝑧
2
1
2
𝜋
Bessel-J
𝜈
1
𝑏
𝑧
Hankel-H-1-Bessel-third-kind
𝜈
𝑎
𝑧
{\displaystyle{\displaystyle\int_{0}^{\infty}Y_{\nu}\left(at\right)J_{\nu+1}%
\left(bt\right)\frac{t\mathrm{d}t}{t^{2}-z^{2}}=\frac{1}{2}\pi J_{\nu+1}\left(%
bz\right){H^{(1)}_{\nu}}\left(az\right),}}
ℜ
ν
>
-
3
2
,
ℑ
z
>
0
formulae-sequence
𝜈
3
2
𝑧
0
{\displaystyle{\displaystyle\Re\nu>-\tfrac{3}{2},\Im z>0}}
a
≥
b
>
0
𝑎
𝑏
0
{\displaystyle{\displaystyle a\geq b>0}}
ℜ
ν
>
-
3
2
,
ℑ
z
>
0
formulae-sequence
𝜈
3
2
𝑧
0
{\displaystyle{\displaystyle\Re\nu>-\tfrac{3}{2},\Im z>0}}
J
ν
(
z
)
Bessel-J
𝜈
𝑧
{\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
Y
ν
(
z
)
Bessel-Y-Weber
𝜈
𝑧
{\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}
H
ν
(
1
)
(
z
)
Hankel-H-1-Bessel-third-kind
𝜈
𝑧
{\displaystyle{\displaystyle{H^{(1)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
ℑ
absent
{\displaystyle{\displaystyle\Im}}
∫
{\displaystyle{\displaystyle\int}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
