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Statements
W
κ
,
μ
(
z
)
=
e
-
1
2
z
2
π
i
∫
-
i
∞
i
∞
Γ
(
1
2
+
μ
+
t
)
Γ
(
1
2
-
μ
+
t
)
Γ
(
-
κ
-
t
)
Γ
(
1
2
+
μ
-
κ
)
Γ
(
1
2
-
μ
-
κ
)
z
-
t
d
t
,
Whittaker-confluent-hypergeometric-W
𝜅
𝜇
𝑧
superscript
𝑒
1
2
𝑧
2
𝜋
imaginary-unit
superscript
subscript
imaginary-unit
imaginary-unit
Euler-Gamma
1
2
𝜇
𝑡
Euler-Gamma
1
2
𝜇
𝑡
Euler-Gamma
𝜅
𝑡
Euler-Gamma
1
2
𝜇
𝜅
Euler-Gamma
1
2
𝜇
𝜅
superscript
𝑧
𝑡
𝑡
{\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=\frac{e^{-\frac{1}{2%
}z}}{2\pi\mathrm{i}}\*\int_{-\mathrm{i}\infty}^{\mathrm{i}\infty}\frac{\Gamma%
\left(\frac{1}{2}+\mu+t\right)\Gamma\left(\frac{1}{2}-\mu+t\right)\Gamma\left(%
-\kappa-t\right)}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)\Gamma\left(\frac{1%
}{2}-\mu-\kappa\right)}z^{-t}\mathrm{d}t,}}
|
ph
z
|
<
3
2
π
phase
𝑧
3
2
𝜋
{\displaystyle{\displaystyle|\operatorname{ph}{z}|<\tfrac{3}{2}\pi}}
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}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∫
{\displaystyle{\displaystyle\int}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
z
𝑧
{\displaystyle{\displaystyle z}}
