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Statements
𝒲
{
M
κ
,
μ
(
z
)
,
W
-
κ
,
μ
(
e
±
π
i
z
)
}
=
Γ
(
1
+
2
μ
)
Γ
(
1
2
+
μ
+
κ
)
e
∓
(
1
2
+
μ
)
π
i
,
Wronskian
Whittaker-confluent-hypergeometric-M
𝜅
𝜇
𝑧
Whittaker-confluent-hypergeometric-W
𝜅
𝜇
superscript
𝑒
plus-or-minus
𝜋
imaginary-unit
𝑧
Euler-Gamma
1
2
𝜇
Euler-Gamma
1
2
𝜇
𝜅
superscript
𝑒
minus-or-plus
1
2
𝜇
𝜋
imaginary-unit
{\displaystyle{\displaystyle\mathscr{W}\left\{M_{\kappa,\mu}\left(z\right),W_{%
-\kappa,\mu}\left(e^{\pm\pi\mathrm{i}}z\right)\right\}=\frac{\Gamma\left(1+2%
\mu\right)}{\Gamma\left(\frac{1}{2}+\mu+\kappa\right)}e^{\mp(\frac{1}{2}+\mu)%
\pi\mathrm{i}},}}
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)}}
W
κ
,
μ
(
z
)
Whittaker-confluent-hypergeometric-W
𝜅
𝜇
𝑧
{\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
𝒲
Wronskian
{\displaystyle{\displaystyle\mathscr{W}}}
π
{\displaystyle{\displaystyle\pi}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
z
𝑧
{\displaystyle{\displaystyle z}}
Identifiers
