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Statements
W
κ
,
μ
(
z
)
=
e
-
1
2
z
z
κ
+
1
Γ
(
1
2
+
μ
-
κ
)
Γ
(
1
2
-
μ
-
κ
)
∫
0
∞
W
-
κ
,
μ
(
t
)
e
-
1
2
t
t
-
κ
-
1
t
+
z
d
t
,
Whittaker-confluent-hypergeometric-W
𝜅
𝜇
𝑧
superscript
𝑒
1
2
𝑧
superscript
𝑧
𝜅
1
Euler-Gamma
1
2
𝜇
𝜅
Euler-Gamma
1
2
𝜇
𝜅
superscript
subscript
0
Whittaker-confluent-hypergeometric-W
𝜅
𝜇
𝑡
superscript
𝑒
1
2
𝑡
superscript
𝑡
𝜅
1
𝑡
𝑧
𝑡
{\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=\frac{e^{-\frac{1}{2%
}z}z^{\kappa+1}}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)\Gamma\left(\frac{1}%
{2}-\mu-\kappa\right)}\*\int_{0}^{\infty}\frac{W_{-\kappa,\mu}\left(t\right)e^%
{-\frac{1}{2}t}t^{-\kappa-1}}{t+z}\mathrm{d}t,}}
|
ph
z
|
<
π
phase
𝑧
𝜋
{\displaystyle{\displaystyle|\operatorname{ph}{z}|<\pi}}
ℜ
(
1
2
+
μ
-
κ
)
>
max
(
2
ℜ
μ
,
0
)
1
2
𝜇
𝜅
2
𝜇
0
{\displaystyle{\displaystyle\Re(\frac{1}{2}+\mu-\kappa)>\max\left(2\Re\mu,0%
\right)}}
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)}}
π
{\displaystyle{\displaystyle\pi}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
∫
{\displaystyle{\displaystyle\int}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
z
𝑧
{\displaystyle{\displaystyle z}}
