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:18.23.E6 - MaRDI portal
Statements
F
1
1
(
a
+
i
x
2
ℜ
a
;
-
i
z
)
F
1
1
(
b
¯
-
i
x
2
ℜ
b
;
i
z
)
=
∑
n
=
0
∞
p
n
(
x
;
a
,
b
,
a
¯
,
b
¯
)
(
2
ℜ
a
)
n
(
2
ℜ
b
)
n
z
n
.
Kummer-confluent-hypergeometric-M-as-1F1
𝑎
imaginary-unit
𝑥
2
𝑎
imaginary-unit
𝑧
Kummer-confluent-hypergeometric-M-as-1F1
𝑏
imaginary-unit
𝑥
2
𝑏
imaginary-unit
𝑧
superscript
subscript
𝑛
0
continuous-Hahn-polynomial-p
𝑛
𝑥
𝑎
𝑏
𝑎
𝑏
Pochhammer
2
𝑎
𝑛
Pochhammer
2
𝑏
𝑛
superscript
𝑧
𝑛
{\displaystyle{\displaystyle{{}_{1}F_{1}}\left({a+\mathrm{i}x\atop 2\Re a};-%
\mathrm{i}z\right){{}_{1}F_{1}}\left({\overline{b}-\mathrm{i}x\atop 2\Re b};%
\mathrm{i}z\right)=\sum_{n=0}^{\infty}\frac{p_{n}\left(x;a,b,\overline{a},%
\overline{b}\right)}{{\left(2\Re a\right)_{n}}{\left(2\Re b\right)_{n}}}z^{n}.}}
F
1
1
(
a
;
b
;
z
)
Kummer-confluent-hypergeometric-M-as-1F1
𝑎
𝑏
𝑧
{\displaystyle{\displaystyle{{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}%
\right)}}
(
a
)
n
Pochhammer
𝑎
𝑛
{\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
z
¯
𝑧
{\displaystyle{\displaystyle\overline{\NVar{z}}}}
p
n
(
x
;
a
,
b
,
a
¯
,
missing
)
continuous-Hahn-polynomial-p
𝑛
𝑥
𝑎
𝑏
𝑎
missing
{\displaystyle{\displaystyle p_{\NVar{n}}\left(\NVar{x};\NVar{a},\NVar{b},%
\NVar{\overline{a}},\NVar{missing}\right)\)\@add@PDF@RDFa@triples\end{document}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
z
𝑧
{\displaystyle{\displaystyle z}}
n
𝑛
{\displaystyle{\displaystyle n}}
x
𝑥
{\displaystyle{\displaystyle x}}
Identifiers
