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Statements
U
(
a
,
z
)
=
2
-
1
4
-
1
2
a
e
-
1
4
z
2
U
(
1
2
a
+
1
4
,
1
2
,
1
2
z
2
)
=
2
-
3
4
-
1
2
a
z
e
-
1
4
z
2
U
(
1
2
a
+
3
4
,
3
2
,
1
2
z
2
)
=
2
-
1
2
a
z
-
1
2
W
-
1
2
a
,
±
1
4
(
1
2
z
2
)
.
parabolic-U
𝑎
𝑧
superscript
2
1
4
1
2
𝑎
superscript
𝑒
1
4
superscript
𝑧
2
Kummer-confluent-hypergeometric-U
1
2
𝑎
1
4
1
2
1
2
superscript
𝑧
2
superscript
2
3
4
1
2
𝑎
𝑧
superscript
𝑒
1
4
superscript
𝑧
2
Kummer-confluent-hypergeometric-U
1
2
𝑎
3
4
3
2
1
2
superscript
𝑧
2
superscript
2
1
2
𝑎
superscript
𝑧
1
2
Whittaker-confluent-hypergeometric-W
1
2
𝑎
plus-or-minus
1
4
1
2
superscript
𝑧
2
{\displaystyle{\displaystyle U\left(a,z\right)=2^{-\frac{1}{4}-\frac{1}{2}a}e^%
{-\frac{1}{4}z^{2}}U\left(\tfrac{1}{2}a+\tfrac{1}{4},\tfrac{1}{2},\tfrac{1}{2}%
z^{2}\right)=2^{-\frac{3}{4}-\frac{1}{2}a}ze^{-\frac{1}{4}z^{2}}U\left(\tfrac{%
1}{2}a+\tfrac{3}{4},\tfrac{3}{2},\tfrac{1}{2}z^{2}\right)=2^{-\frac{1}{2}a}z^{%
-\frac{1}{2}}W_{-\frac{1}{2}a,\pm\frac{1}{4}}\left(\tfrac{1}{2}z^{2}\right).}}
U
(
a
,
b
,
z
)
Kummer-confluent-hypergeometric-U
𝑎
𝑏
𝑧
{\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
W
κ
,
μ
(
z
)
Whittaker-confluent-hypergeometric-W
𝜅
𝜇
𝑧
{\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
U
(
a
,
z
)
parabolic-U
𝑎
𝑧
{\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}
z
𝑧
{\displaystyle{\displaystyle z}}
a
𝑎
{\displaystyle{\displaystyle a}}
Identifiers
