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Statements
1
Γ
(
1
+
2
μ
)
2
π
i
∫
-
∞
(
0
+
)
e
z
t
+
1
2
t
-
1
t
κ
M
κ
,
μ
(
t
-
1
)
d
t
=
z
-
κ
-
1
2
Γ
(
1
2
+
μ
-
κ
)
I
2
μ
(
2
z
)
,
1
Euler-Gamma
1
2
𝜇
2
𝜋
imaginary-unit
superscript
subscript
limit-from
0
superscript
𝑒
𝑧
𝑡
1
2
superscript
𝑡
1
superscript
𝑡
𝜅
Whittaker-confluent-hypergeometric-M
𝜅
𝜇
superscript
𝑡
1
𝑡
superscript
𝑧
𝜅
1
2
Euler-Gamma
1
2
𝜇
𝜅
modified-Bessel-first-kind
2
𝜇
2
𝑧
{\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)2\pi\mathrm{i}}%
\int_{-\infty}^{(0+)}e^{zt+\frac{1}{2}t^{-1}}t^{\kappa}M_{\kappa,\mu}\left(t^{%
-1}\right)\mathrm{d}t=\frac{z^{-\kappa-\frac{1}{2}}}{\Gamma\left(\frac{1}{2}+%
\mu-\kappa\right)}I_{2\mu}\left(2\sqrt{z}\right),}}
ℜ
z
>
0
𝑧
0
{\displaystyle{\displaystyle\Re z>0}}
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)}}
π
{\displaystyle{\displaystyle\pi}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∫
{\displaystyle{\displaystyle\int}}
I
ν
(
z
)
modified-Bessel-first-kind
𝜈
𝑧
{\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
z
𝑧
{\displaystyle{\displaystyle z}}
Identifiers
