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Statements
1
Γ
(
1
+
2
μ
)
∫
0
∞
e
-
1
2
t
t
ν
-
1
M
κ
,
μ
(
t
)
d
t
=
Γ
(
μ
+
ν
+
1
2
)
Γ
(
κ
-
ν
)
Γ
(
1
2
+
μ
+
κ
)
Γ
(
1
2
+
μ
-
ν
)
,
1
Euler-Gamma
1
2
𝜇
superscript
subscript
0
superscript
𝑒
1
2
𝑡
superscript
𝑡
𝜈
1
Whittaker-confluent-hypergeometric-M
𝜅
𝜇
𝑡
𝑡
Euler-Gamma
𝜇
𝜈
1
2
Euler-Gamma
𝜅
𝜈
Euler-Gamma
1
2
𝜇
𝜅
Euler-Gamma
1
2
𝜇
𝜈
{\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)}\int_{0}^{%
\infty}e^{-\frac{1}{2}t}t^{\nu-1}M_{\kappa,\mu}\left(t\right)\mathrm{d}t=\frac%
{\Gamma\left(\mu+\nu+\frac{1}{2}\right)\Gamma\left(\kappa-\nu\right)}{\Gamma%
\left(\frac{1}{2}+\mu+\kappa\right)\Gamma\left(\frac{1}{2}+\mu-\nu\right)},}}
-
1
2
-
ℜ
μ
<
ℜ
ν
<
ℜ
κ
1
2
𝜇
𝜈
𝜅
{\displaystyle{\displaystyle-\tfrac{1}{2}-\Re\mu<\Re\nu<\Re\kappa}}
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}}
Identifiers
