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