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:10.68.E9 - MaRDI portal
Statements
bei
ν
′
x
=
1
2
M
ν
+
1
sin
(
θ
ν
+
1
-
1
4
π
)
-
1
2
M
ν
-
1
sin
(
θ
ν
-
1
-
1
4
π
)
=
(
ν
/
x
)
M
ν
sin
θ
ν
+
M
ν
+
1
sin
(
θ
ν
+
1
-
1
4
π
)
=
-
(
ν
/
x
)
M
ν
sin
θ
ν
-
M
ν
-
1
sin
(
θ
ν
-
1
-
1
4
π
)
.
diffop
Kelvin-bei
𝜈
1
𝑥
1
2
modulus-Bessel-M
𝜈
1
phase-Bessel-Theta
𝜈
1
1
4
𝜋
1
2
modulus-Bessel-M
𝜈
1
phase-Bessel-Theta
𝜈
1
1
4
𝜋
𝜈
𝑥
modulus-Bessel-M
𝜈
phase-Bessel-Theta
𝜈
modulus-Bessel-M
𝜈
1
phase-Bessel-Theta
𝜈
1
1
4
𝜋
𝜈
𝑥
modulus-Bessel-M
𝜈
phase-Bessel-Theta
𝜈
modulus-Bessel-M
𝜈
1
phase-Bessel-Theta
𝜈
1
1
4
𝜋
{\displaystyle{\displaystyle\operatorname{bei}_{\nu}'x=\tfrac{1}{2}M_{\nu+1}%
\sin\left(\theta_{\nu+1}-\tfrac{1}{4}\pi\right)-\tfrac{1}{2}M_{\nu-1}\sin\left%
(\theta_{\nu-1}-\tfrac{1}{4}\pi\right)=(\nu/x)M_{\nu}\sin\theta_{\nu}+M_{\nu+1%
}\sin\left(\theta_{\nu+1}-\tfrac{1}{4}\pi\right)=-(\nu/x)M_{\nu}\sin\theta_{%
\nu}-M_{\nu-1}\sin\left(\theta_{\nu-1}-\tfrac{1}{4}\pi\right).}}
bei
ν
(
x
)
Kelvin-bei
𝜈
𝑥
{\displaystyle{\displaystyle\operatorname{bei}_{\NVar{\nu}}\left(\NVar{x}%
\right)}}
π
{\displaystyle{\displaystyle\pi}}
M
ν
(
x
)
modulus-Bessel-M
𝜈
𝑥
{\displaystyle{\displaystyle M_{\NVar{\nu}}\left(\NVar{x}\right)}}
θ
ν
(
x
)
phase-Bessel-Theta
𝜈
𝑥
{\displaystyle{\displaystyle\theta_{\NVar{\nu}}\left(\NVar{x}\right)}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
x
𝑥
{\displaystyle{\displaystyle x}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
