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Statements
F
2
0
(
-
;
1
,
1
;
x
)
=
∫
-
1
/
2
∞
x
t
(
Γ
(
t
+
1
)
)
3
d
t
+
2
ℜ
∫
-
1
/
2
i
∞
x
t
(
Γ
(
t
+
1
)
)
3
d
t
e
-
2
π
i
t
-
1
=
∫
0
∞
x
t
(
Γ
(
t
+
1
)
)
3
d
t
+
O
(
1
)
,
Gauss-hypergeometric-pFq
0
2
1
1
𝑥
superscript
subscript
1
2
superscript
𝑥
𝑡
superscript
Euler-Gamma
𝑡
1
3
𝑡
2
superscript
subscript
1
2
𝑖
superscript
𝑥
𝑡
superscript
Euler-Gamma
𝑡
1
3
𝑡
superscript
𝑒
2
𝜋
𝑖
𝑡
1
superscript
subscript
0
superscript
𝑥
𝑡
superscript
Euler-Gamma
𝑡
1
3
𝑡
Big-O
1
{\displaystyle{\displaystyle{{}_{0}F_{2}}\left(-;1,1;x\right)=\int_{-1/2}^{%
\infty}\frac{x^{t}}{(\Gamma\left(t+1\right))^{3}}\mathrm{d}t+2\Re\int_{-1/2}^{%
i\infty}\frac{x^{t}}{(\Gamma\left(t+1\right))^{3}}\frac{\mathrm{d}t}{e^{-2\pi
it%
}-1}=\int_{0}^{\infty}\frac{x^{t}}{(\Gamma\left(t+1\right))^{3}}\mathrm{d}t+O%
\left(1\right),}}
x
→
+
∞
→
𝑥
{\displaystyle{\displaystyle x\to+\infty}}
O
(
x
)
Big-O
𝑥
{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
F
q
p
(
a
1
,
…
,
a
p
;
b
1
,
…
,
b
q
;
z
)
Gauss-hypergeometric-pFq
𝑝
𝑞
subscript
𝑎
1
…
subscript
𝑎
𝑝
subscript
𝑏
1
…
subscript
𝑏
𝑞
𝑧
{\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots%
,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∫
{\displaystyle{\displaystyle\int}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
Identifiers
