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:10.38.E6 - MaRDI portal
Statements
∂
I
ν
(
x
)
∂
ν
|
ν
=
±
1
2
=
-
1
2
π
x
(
E
1
(
2
x
)
e
x
±
Ei
(
2
x
)
e
-
x
)
,
evaluated-at
partial-derivative
modified-Bessel-first-kind
𝜈
𝑥
𝜈
𝜈
plus-or-minus
1
2
1
2
𝜋
𝑥
plus-or-minus
exponential-integral
2
𝑥
superscript
𝑒
𝑥
exponential-integral-Ei
2
𝑥
superscript
𝑒
𝑥
{\displaystyle{\displaystyle\left.\frac{\partial I_{\nu}\left(x\right)}{%
\partial\nu}\right|_{\nu=\pm\frac{1}{2}}=-\frac{1}{\sqrt{2\pi x}}\left(E_{1}%
\left(2x\right)e^{x}\pm\mathrm{Ei}\left(2x\right)e^{-x}\right),}}
π
{\displaystyle{\displaystyle\pi}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
E
1
(
z
)
exponential-integral
𝑧
{\displaystyle{\displaystyle E_{1}\left(\NVar{z}\right)}}
Ei
(
x
)
exponential-integral-Ei
𝑥
{\displaystyle{\displaystyle\mathrm{Ei}\left(\NVar{x}\right)}}
I
ν
(
z
)
modified-Bessel-first-kind
𝜈
𝑧
{\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
∂
f
∂
x
partial-derivative
𝑓
𝑥
{\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
∂
x
𝑥
{\displaystyle{\displaystyle\partial\NVar{x}}}
x
𝑥
{\displaystyle{\displaystyle x}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
