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