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