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Statements
∫
0
∞
e
-
z
t
t
μ
-
1
2
M
κ
,
μ
(
t
)
d
t
=
Γ
(
2
μ
+
1
)
(
z
+
1
2
)
-
κ
-
μ
-
1
2
(
z
-
1
2
)
κ
-
μ
-
1
2
,
superscript
subscript
0
superscript
𝑒
𝑧
𝑡
superscript
𝑡
𝜇
1
2
Whittaker-confluent-hypergeometric-M
𝜅
𝜇
𝑡
𝑡
Euler-Gamma
2
𝜇
1
superscript
𝑧
1
2
𝜅
𝜇
1
2
superscript
𝑧
1
2
𝜅
𝜇
1
2
{\displaystyle{\displaystyle\int_{0}^{\infty}e^{-zt}t^{\mu-\frac{1}{2}}M_{%
\kappa,\mu}\left(t\right)\mathrm{d}t=\Gamma\left(2\mu+1\right)\left(z+\tfrac{1%
}{2}\right)^{-\kappa-\mu-\frac{1}{2}}\*\left(z-\tfrac{1}{2}\right)^{\kappa-\mu%
-\frac{1}{2}},}}
ℜ
μ
>
-
1
2
𝜇
1
2
{\displaystyle{\displaystyle\Re\mu>-\tfrac{1}{2}}}
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)}}
M
κ
,
μ
(
z
)
Whittaker-confluent-hypergeometric-M
𝜅
𝜇
𝑧
{\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
∫
{\displaystyle{\displaystyle\int}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
z
𝑧
{\displaystyle{\displaystyle z}}
