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Statements
1
Γ
(
b
)
M
(
a
,
b
,
z
)
=
e
∓
a
π
i
Γ
(
b
-
a
)
U
(
a
,
b
,
z
)
+
e
±
(
b
-
a
)
π
i
Γ
(
a
)
e
z
U
(
b
-
a
,
b
,
e
±
π
i
z
)
.
1
Euler-Gamma
𝑏
Kummer-confluent-hypergeometric-M
𝑎
𝑏
𝑧
superscript
𝑒
minus-or-plus
𝑎
𝜋
imaginary-unit
Euler-Gamma
𝑏
𝑎
Kummer-confluent-hypergeometric-U
𝑎
𝑏
𝑧
superscript
𝑒
plus-or-minus
𝑏
𝑎
𝜋
imaginary-unit
Euler-Gamma
𝑎
superscript
𝑒
𝑧
Kummer-confluent-hypergeometric-U
𝑏
𝑎
𝑏
superscript
𝑒
plus-or-minus
𝜋
imaginary-unit
𝑧
{\displaystyle{\displaystyle\frac{1}{\Gamma\left(b\right)}M\left(a,b,z\right)=%
\frac{e^{\mp a\pi\mathrm{i}}}{\Gamma\left(b-a\right)}U\left(a,b,z\right)+\frac%
{e^{\pm(b-a)\pi\mathrm{i}}}{\Gamma\left(a\right)}e^{z}U\left(b-a,b,e^{\pm\pi%
\mathrm{i}}z\right).}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
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)}}
π
{\displaystyle{\displaystyle\pi}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
z
𝑧
{\displaystyle{\displaystyle z}}
Identifiers
