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Statements
∫
0
∞
e
-
z
t
t
ν
-
1
W
κ
,
μ
(
t
)
d
t
=
Γ
(
1
2
+
μ
+
ν
)
Γ
(
1
2
-
μ
+
ν
)
𝐅
1
2
(
1
2
-
μ
+
ν
,
1
2
+
μ
+
ν
ν
-
κ
+
1
;
1
2
-
z
)
,
superscript
subscript
0
superscript
𝑒
𝑧
𝑡
superscript
𝑡
𝜈
1
Whittaker-confluent-hypergeometric-W
𝜅
𝜇
𝑡
𝑡
Euler-Gamma
1
2
𝜇
𝜈
Euler-Gamma
1
2
𝜇
𝜈
hypergeometric-bold-pFq
2
1
1
2
𝜇
𝜈
1
2
𝜇
𝜈
𝜈
𝜅
1
1
2
𝑧
{\displaystyle{\displaystyle\int_{0}^{\infty}e^{-zt}t^{\nu-1}W_{\kappa,\mu}%
\left(t\right)\mathrm{d}t=\Gamma\left(\tfrac{1}{2}+\mu+\nu\right)\Gamma\left(%
\tfrac{1}{2}-\mu+\nu\right)\*{{}_{2}{\mathbf{F}}_{1}}\left({\tfrac{1}{2}-\mu+%
\nu,\tfrac{1}{2}+\mu+\nu\atop\nu-\kappa+1};\tfrac{1}{2}-z\right),}}
ℜ
(
ν
+
1
2
)
>
|
ℜ
μ
|
𝜈
1
2
𝜇
{\displaystyle{\displaystyle\Re(\nu+\tfrac{1}{2})>|\Re\mu|}}
ℜ
z
>
-
1
2
𝑧
1
2
{\displaystyle{\displaystyle\Re z>-\tfrac{1}{2}}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
W
κ
,
μ
(
z
)
Whittaker-confluent-hypergeometric-W
𝜅
𝜇
𝑧
{\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
𝐅
q
p
(
𝐚
;
𝐛
;
)
hypergeometric-bold-pFq
𝑝
𝑞
𝐚
𝐛
{\displaystyle{\displaystyle{{}_{\NVar{p}}{\mathbf{F}}_{\NVar{q}}}\left(\NVar{%
\mathbf{a}};\NVar{\mathbf{b}};\right)\)\@add@PDF@RDFa@triples\end{document}}}
∫
{\displaystyle{\displaystyle\int}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
z
𝑧
{\displaystyle{\displaystyle z}}
Identifiers
