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DLMF:13.2.E35 - MaRDI portal
Statements
π²
β‘
{
π
β‘
(
a
,
b
,
z
)
,
e
z
β’
U
β‘
(
b
-
a
,
b
,
e
Β±
Ο
β’
i
β’
z
)
}
=
e
β
b
β’
Ο
β’
i
β’
z
-
b
β’
e
z
/
Ξ
β‘
(
b
-
a
)
,
Wronskian
Kummer-confluent-hypergeometric-bold-M
π
π
π§
superscript
π
π§
Kummer-confluent-hypergeometric-U
π
π
π
superscript
π
plus-or-minus
π
imaginary-unit
π§
superscript
π
minus-or-plus
π
π
imaginary-unit
superscript
π§
π
superscript
π
π§
Euler-Gamma
π
π
{\displaystyle{\displaystyle\mathscr{W}\left\{{\mathbf{M}}\left(a,b,z\right),e%
^{z}U\left(b-a,b,e^{\pm\pi\mathrm{i}}z\right)\right\}=\ifrac{e^{\mp b\pi%
\mathrm{i}}z^{-b}e^{z}}{\Gamma\left(b-a\right)},}}
Ξ
β‘
(
z
)
Euler-Gamma
π§
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
U
β‘
(
a
,
b
,
z
)
Kummer-confluent-hypergeometric-U
π
π
π§
{\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
π
β‘
(
a
,
b
,
z
)
Kummer-confluent-hypergeometric-bold-M
π
π
π§
{\displaystyle{\displaystyle{\mathbf{M}}\left(\NVar{a},\NVar{b},\NVar{z}\right%
)}}
π²
Wronskian
{\displaystyle{\displaystyle\mathscr{W}}}
Ο
{\displaystyle{\displaystyle\pi}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
z
π§
{\displaystyle{\displaystyle z}}
Identifiers