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Statements
W
κ
,
±
1
2
n
(
z
)
=
(
-
1
)
κ
-
1
2
n
-
1
2
e
-
1
2
z
z
1
2
n
+
1
2
∑
k
=
0
κ
-
1
2
n
-
1
2
(
κ
-
1
2
n
-
1
2
k
)
(
n
+
1
+
k
)
κ
-
k
-
1
2
n
-
1
2
(
-
z
)
k
,
Whittaker-confluent-hypergeometric-W
𝜅
plus-or-minus
1
2
𝑛
𝑧
superscript
1
𝜅
1
2
𝑛
1
2
superscript
𝑒
1
2
𝑧
superscript
𝑧
1
2
𝑛
1
2
superscript
subscript
𝑘
0
𝜅
1
2
𝑛
1
2
binomial
𝜅
1
2
𝑛
1
2
𝑘
Pochhammer
𝑛
1
𝑘
𝜅
𝑘
1
2
𝑛
1
2
superscript
𝑧
𝑘
{\displaystyle{\displaystyle W_{\kappa,\pm\frac{1}{2}n}\left(z\right)=(-1)^{%
\kappa-\frac{1}{2}n-\frac{1}{2}}e^{-\frac{1}{2}z}z^{\frac{1}{2}n+\frac{1}{2}}%
\sum_{k=0}^{\kappa-\frac{1}{2}n-\frac{1}{2}}\genfrac{(}{)}{0.0pt}{}{\kappa-%
\frac{1}{2}n-\frac{1}{2}}{k}{\left(n+1+k\right)_{\kappa-k-\frac{1}{2}n-\frac{1%
}{2}}}(-z)^{k},}}
κ
-
1
2
n
-
1
2
=
0
,
1
,
2
,
…
𝜅
1
2
𝑛
1
2
0
1
2
…
{\displaystyle{\displaystyle\kappa-\frac{1}{2}n-\frac{1}{2}=0,1,2,\dots}}
(
a
)
n
Pochhammer
𝑎
𝑛
{\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
W
κ
,
μ
(
z
)
Whittaker-confluent-hypergeometric-W
𝜅
𝜇
𝑧
{\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
(
m
n
)
binomial
𝑚
𝑛
{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
n
𝑛
{\displaystyle{\displaystyle n}}
z
𝑧
{\displaystyle{\displaystyle z}}
Identifiers
