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Statements
M
κ
,
μ
(
z
)
=
Γ
(
1
+
2
μ
)
z
λ
Γ
(
1
+
2
μ
-
2
λ
)
Γ
(
2
λ
)
∫
0
1
M
κ
-
λ
,
μ
-
λ
(
z
t
)
e
1
2
z
(
t
-
1
)
t
μ
-
λ
-
1
2
(
1
-
t
)
2
λ
-
1
d
t
,
Whittaker-confluent-hypergeometric-M
𝜅
𝜇
𝑧
Euler-Gamma
1
2
𝜇
superscript
𝑧
𝜆
Euler-Gamma
1
2
𝜇
2
𝜆
Euler-Gamma
2
𝜆
superscript
subscript
0
1
Whittaker-confluent-hypergeometric-M
𝜅
𝜆
𝜇
𝜆
𝑧
𝑡
superscript
𝑒
1
2
𝑧
𝑡
1
superscript
𝑡
𝜇
𝜆
1
2
superscript
1
𝑡
2
𝜆
1
𝑡
{\displaystyle{\displaystyle M_{\kappa,\mu}\left(z\right)=\frac{\Gamma\left(1+%
2\mu\right)z^{\lambda}}{\Gamma\left(1+2\mu-2\lambda\right)\Gamma\left(2\lambda%
\right)}\*\int_{0}^{1}M_{\kappa-\lambda,\mu-\lambda}\left(zt\right)e^{\frac{1}%
{2}z(t-1)}t^{\mu-\lambda-\frac{1}{2}}{(1-t)^{2\lambda-1}}\mathrm{d}t,}}
ℜ
μ
+
1
2
>
ℜ
λ
>
0
𝜇
1
2
𝜆
0
{\displaystyle{\displaystyle\Re\mu+\tfrac{1}{2}>\Re\lambda>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)}}
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
