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Statements
π
β‘
(
a
,
b
,
z
)
=
e
-
a
β’
Ο
β’
i
β’
Ξ
β‘
(
1
-
a
)
2
β’
Ο
β’
i
β’
Ξ
β‘
(
b
-
a
)
β’
β«
1
(
0
+
)
e
z
β’
t
β’
t
a
-
1
β’
(
1
-
t
)
b
-
a
-
1
β’
d
t
,
Kummer-confluent-hypergeometric-bold-M
π
π
π§
superscript
π
π
π
imaginary-unit
Euler-Gamma
1
π
2
π
imaginary-unit
Euler-Gamma
π
π
superscript
subscript
1
limit-from
0
superscript
π
π§
π‘
superscript
π‘
π
1
superscript
1
π‘
π
π
1
π‘
{\displaystyle{\displaystyle{\mathbf{M}}\left(a,b,z\right)=e^{-a\pi\mathrm{i}}%
\frac{\Gamma\left(1-a\right)}{2\pi\mathrm{i}\Gamma\left(b-a\right)}\int_{1}^{(%
0+)}e^{zt}t^{a-1}{(1-t)^{b-a-1}}\mathrm{d}t,}}
β
β‘
(
b
-
a
)
>
0
π
π
0
{\displaystyle{\displaystyle\Re(b-a)>0}}
a
β
1
,
2
,
3
,
β¦
π
1
2
3
β¦
{\displaystyle{\displaystyle a\neq 1,2,3,\dots}}
β
β‘
(
b
-
a
)
>
0
π
π
0
{\displaystyle{\displaystyle\Re(b-a)>0}}
Ξ
β‘
(
z
)
Euler-Gamma
π§
{\displaystyle{\displaystyle\Gamma\left(\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%
)}}
Ο
{\displaystyle{\displaystyle\pi}}
d
x
π₯
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
β«
{\displaystyle{\displaystyle\int}}
β
β‘
absent
{\displaystyle{\displaystyle\Re}}
z
π§
{\displaystyle{\displaystyle z}}
Identifiers
