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:10.17.E13 - MaRDI portal
Statements
H
ν
(
1
)
(
z
)
H
ν
(
2
)
(
z
)
}
=
(
2
π
z
)
1
2
e
±
i
ω
(
∑
k
=
0
ℓ
-
1
(
±
i
)
k
a
k
(
ν
)
z
k
+
R
ℓ
±
(
ν
,
z
)
)
,
selection
Hankel-H-1-Bessel-third-kind
𝜈
𝑧
Hankel-H-2-Bessel-third-kind
𝜈
𝑧
superscript
2
𝜋
𝑧
1
2
superscript
𝑒
plus-or-minus
𝑖
𝜔
superscript
subscript
𝑘
0
ℓ
1
superscript
plus-or-minus
𝑖
𝑘
subscript
𝑎
𝑘
𝜈
superscript
𝑧
𝑘
superscript
subscript
𝑅
ℓ
plus-or-minus
𝜈
𝑧
{\displaystyle{\displaystyle\rselection{{H^{(1)}_{\nu}}\left(z\right)\\
{H^{(2)}_{\nu}}\left(z\right)}=\left(\frac{2}{\pi z}\right)^{\frac{1}{2}}e^{%
\pm i\omega}\left(\sum_{k=0}^{\ell-1}(\pm i)^{k}\frac{a_{k}(\nu)}{z^{k}}+R_{%
\ell}^{\pm}(\nu,z)\right),}}
ℓ
=
1
,
2
,
…
ℓ
1
2
…
{\displaystyle{\displaystyle\ell=1,2,\ldots}}
H
ν
(
1
)
(
z
)
Hankel-H-1-Bessel-third-kind
𝜈
𝑧
{\displaystyle{\displaystyle{H^{(1)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}
H
ν
(
2
)
(
z
)
Hankel-H-2-Bessel-third-kind
𝜈
𝑧
{\displaystyle{\displaystyle{H^{(2)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
k
𝑘
{\displaystyle{\displaystyle k}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
a
k
(
ν
)
subscript
𝑎
𝑘
𝜈
{\displaystyle{\displaystyle a_{k}(\nu)}}
ω
𝜔
{\displaystyle{\displaystyle\omega}}
R
ℓ
±
(
ν
,
z
)
superscript
subscript
𝑅
ℓ
plus-or-minus
𝜈
𝑧
{\displaystyle{\displaystyle R_{\ell}^{\pm}(\nu,z)}}
Identifiers
