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:10.9.E29 - MaRDI portal
Statements
J
μ
(
x
)
J
ν
(
x
)
=
1
2
π
i
∫
-
i
∞
i
∞
Γ
(
-
t
)
Γ
(
2
t
+
μ
+
ν
+
1
)
(
1
2
x
)
μ
+
ν
+
2
t
Γ
(
t
+
μ
+
1
)
Γ
(
t
+
ν
+
1
)
Γ
(
t
+
μ
+
ν
+
1
)
d
t
,
Bessel-J
𝜇
𝑥
Bessel-J
𝜈
𝑥
1
2
𝜋
𝑖
superscript
subscript
𝑖
𝑖
Euler-Gamma
𝑡
Euler-Gamma
2
𝑡
𝜇
𝜈
1
superscript
1
2
𝑥
𝜇
𝜈
2
𝑡
Euler-Gamma
𝑡
𝜇
1
Euler-Gamma
𝑡
𝜈
1
Euler-Gamma
𝑡
𝜇
𝜈
1
𝑡
{\displaystyle{\displaystyle J_{\mu}\left(x\right)J_{\nu}\left(x\right)=\frac{%
1}{2\pi i}\int_{-i\infty}^{i\infty}\frac{\Gamma\left(-t\right)\Gamma\left(2t+%
\mu+\nu+1\right)(\tfrac{1}{2}x)^{\mu+\nu+2t}}{\Gamma\left(t+\mu+1\right)\Gamma%
\left(t+\nu+1\right)\Gamma\left(t+\mu+\nu+1\right)}\mathrm{d}t,}}
x
>
0
𝑥
0
{\displaystyle{\displaystyle x>0}}
J
ν
(
z
)
Bessel-J
𝜈
𝑧
{\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∫
{\displaystyle{\displaystyle\int}}
x
𝑥
{\displaystyle{\displaystyle x}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
