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:13.15.E16 - MaRDI portal
Statements
d
n
d
z
n
(
e
1
2
z
z
-
μ
-
1
2
M
κ
,
μ
(
z
)
)
=
(
1
2
+
μ
-
κ
)
n
(
1
+
2
μ
)
n
e
1
2
z
z
-
μ
-
1
2
(
n
+
1
)
M
κ
-
1
2
n
,
μ
+
1
2
n
(
z
)
,
derivative
𝑧
𝑛
superscript
𝑒
1
2
𝑧
superscript
𝑧
𝜇
1
2
Whittaker-confluent-hypergeometric-M
𝜅
𝜇
𝑧
Pochhammer
1
2
𝜇
𝜅
𝑛
Pochhammer
1
2
𝜇
𝑛
superscript
𝑒
1
2
𝑧
superscript
𝑧
𝜇
1
2
𝑛
1
Whittaker-confluent-hypergeometric-M
𝜅
1
2
𝑛
𝜇
1
2
𝑛
𝑧
{\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(e^%
{\frac{1}{2}z}z^{-\mu-\frac{1}{2}}M_{\kappa,\mu}\left(z\right)\right)=\frac{{%
\left(\frac{1}{2}+\mu-\kappa\right)_{n}}}{{\left(1+2\mu\right)_{n}}}e^{\frac{1%
}{2}z}z^{-\mu-\frac{1}{2}(n+1)}M_{\kappa-\frac{1}{2}n,\mu+\frac{1}{2}n}\left(z%
\right),}}
(
a
)
n
Pochhammer
𝑎
𝑛
{\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
M
κ
,
μ
(
z
)
Whittaker-confluent-hypergeometric-M
𝜅
𝜇
𝑧
{\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
d
f
d
x
derivative
𝑓
𝑥
{\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
n
𝑛
{\displaystyle{\displaystyle n}}
z
𝑧
{\displaystyle{\displaystyle z}}
Identifiers
