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Statements
(
z
d
d
z
z
)
n
(
e
1
2
z
z
-
κ
-
1
W
κ
,
μ
(
z
)
)
=
(
1
2
+
μ
-
κ
)
n
(
1
2
-
μ
-
κ
)
n
e
1
2
z
z
n
-
κ
-
1
W
κ
-
n
,
μ
(
z
)
,
superscript
𝑧
derivative
𝑧
𝑧
𝑛
superscript
𝑒
1
2
𝑧
superscript
𝑧
𝜅
1
Whittaker-confluent-hypergeometric-W
𝜅
𝜇
𝑧
Pochhammer
1
2
𝜇
𝜅
𝑛
Pochhammer
1
2
𝜇
𝜅
𝑛
superscript
𝑒
1
2
𝑧
superscript
𝑧
𝑛
𝜅
1
Whittaker-confluent-hypergeometric-W
𝜅
𝑛
𝜇
𝑧
{\displaystyle{\displaystyle\left(z\frac{\mathrm{d}}{\mathrm{d}z}z\right)^{n}%
\left(e^{\frac{1}{2}z}z^{-\kappa-1}W_{\kappa,\mu}\left(z\right)\right)={\left(%
\tfrac{1}{2}+\mu-\kappa\right)_{n}}{\left(\tfrac{1}{2}-\mu-\kappa\right)_{n}}e%
^{\frac{1}{2}z}z^{n-\kappa-1}W_{\kappa-n,\mu}\left(z\right),}}
(
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)}}
d
f
d
x
derivative
𝑓
𝑥
{\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
n
𝑛
{\displaystyle{\displaystyle n}}
z
𝑧
{\displaystyle{\displaystyle z}}
Identifiers
