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Statements
M
κ
,
μ
(
z
)
=
Γ
(
1
+
2
μ
)
z
μ
+
1
2
2
-
2
μ
Γ
(
1
2
+
μ
-
κ
)
Γ
(
1
2
+
μ
+
κ
)
∫
-
1
1
e
1
2
z
t
(
1
+
t
)
μ
-
1
2
-
κ
(
1
-
t
)
μ
-
1
2
+
κ
d
t
,
Whittaker-confluent-hypergeometric-M
𝜅
𝜇
𝑧
Euler-Gamma
1
2
𝜇
superscript
𝑧
𝜇
1
2
superscript
2
2
𝜇
Euler-Gamma
1
2
𝜇
𝜅
Euler-Gamma
1
2
𝜇
𝜅
superscript
subscript
1
1
superscript
𝑒
1
2
𝑧
𝑡
superscript
1
𝑡
𝜇
1
2
𝜅
superscript
1
𝑡
𝜇
1
2
𝜅
𝑡
{\displaystyle{\displaystyle M_{\kappa,\mu}\left(z\right)=\frac{\Gamma\left(1+%
2\mu\right)z^{\mu+\frac{1}{2}}2^{-2\mu}}{\Gamma\left(\frac{1}{2}+\mu-\kappa%
\right)\Gamma\left(\frac{1}{2}+\mu+\kappa\right)}\*\int_{-1}^{1}e^{\frac{1}{2}%
zt}(1+t)^{\mu-\frac{1}{2}-\kappa}(1-t)^{\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}>\left|\Re\kappa\right|}}
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}}
z
𝑧
{\displaystyle{\displaystyle z}}
Identifiers
