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Statements
(
z
d
d
z
z
)
n
(
e
-
1
2
z
z
κ
-
1
M
κ
,
μ
(
z
)
)
=
(
1
2
+
μ
+
κ
)
n
e
-
1
2
z
z
κ
+
n
-
1
M
κ
+
n
,
μ
(
z
)
.
superscript
𝑧
derivative
𝑧
𝑧
𝑛
superscript
𝑒
1
2
𝑧
superscript
𝑧
𝜅
1
Whittaker-confluent-hypergeometric-M
𝜅
𝜇
𝑧
Pochhammer
1
2
𝜇
𝜅
𝑛
superscript
𝑒
1
2
𝑧
superscript
𝑧
𝜅
𝑛
1
Whittaker-confluent-hypergeometric-M
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}M_{\kappa,\mu}\left(z\right)\right)={\left(%
\tfrac{1}{2}+\mu+\kappa\right)_{n}}e^{-\frac{1}{2}z}z^{\kappa+n-1}\*M_{\kappa+%
n,\mu}\left(z\right).}}
(
a
)
n
Pochhammer
𝑎
𝑛
{\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
M
κ
,
μ
(
z
)
Whittaker-confluent-hypergeometric-M
𝜅
𝜇
𝑧
{\displaystyle{\displaystyle M_{\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}}
