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