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Statements
U
(
a
,
a
+
n
+
1
,
z
)
=
(
-
1
)
n
(
1
-
a
-
n
)
n
z
a
+
n
M
(
-
n
,
1
-
a
-
n
,
z
)
=
z
-
a
∑
s
=
0
n
(
n
s
)
(
a
)
s
z
-
s
.
Kummer-confluent-hypergeometric-U
𝑎
𝑎
𝑛
1
𝑧
superscript
1
𝑛
Pochhammer
1
𝑎
𝑛
𝑛
superscript
𝑧
𝑎
𝑛
Kummer-confluent-hypergeometric-M
𝑛
1
𝑎
𝑛
𝑧
superscript
𝑧
𝑎
superscript
subscript
𝑠
0
𝑛
binomial
𝑛
𝑠
Pochhammer
𝑎
𝑠
superscript
𝑧
𝑠
{\displaystyle{\displaystyle U\left(a,a+n+1,z\right)=\frac{(-1)^{n}{\left(1-a-%
n\right)_{n}}}{z^{a+n}}M\left(-n,1-a-n,z\right)=z^{-a}\sum_{s=0}^{n}\genfrac{(%
}{)}{0.0pt}{}{n}{s}{\left(a\right)_{s}}z^{-s}.}}
M
(
a
,
b
,
z
)
Kummer-confluent-hypergeometric-M
𝑎
𝑏
𝑧
{\displaystyle{\displaystyle M\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
U
(
a
,
b
,
z
)
Kummer-confluent-hypergeometric-U
𝑎
𝑏
𝑧
{\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
(
a
)
n
Pochhammer
𝑎
𝑛
{\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
(
m
n
)
binomial
𝑚
𝑛
{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
n
𝑛
{\displaystyle{\displaystyle n}}
s
𝑠
{\displaystyle{\displaystyle s}}
z
𝑧
{\displaystyle{\displaystyle z}}
