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Statements
π
β‘
(
a
,
b
,
z
)
=
e
-
b
β’
Ο
β’
i
β’
Ξ
β‘
(
1
-
a
)
β’
Ξ
β‘
(
1
+
a
-
b
)
β’
1
4
β’
Ο
2
β’
β«
Ξ±
(
0
+
,
1
+
,
0
-
,
1
-
)
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
Euler-Gamma
1
π
π
1
4
superscript
π
2
superscript
subscript
πΌ
limit-from
0
limit-from
1
limit-from
0
limit-from
1
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^{-b\pi\mathrm{i}}%
\Gamma\left(1-a\right)\Gamma\left(1+a-b\right)\*\frac{1}{4\pi^{2}}\int_{\alpha%
}^{(0+,1+,0-,1-)}e^{zt}t^{a-1}{(1-t)^{b-a-1}}\mathrm{d}t,}}
a
,
b
-
a
β
1
,
2
,
3
,
β¦
formulae-sequence
π
π
π
1
2
3
β¦
{\displaystyle{\displaystyle a,b-a\neq 1,2,3,\dots}}
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}}
z
π§
{\displaystyle{\displaystyle z}}
Identifiers
