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Statements
F
1
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β
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β
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γ
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x
,
y
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=
Γ
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γ
)
Γ
(
α
)
Γ
(
γ
-
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∫
0
1
u
α
-
1
(
1
-
u
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γ
-
α
-
1
(
1
-
u
x
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β
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1
-
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β
′
d
u
,
Appell-F-1
𝛼
𝛽
superscript
𝛽
′
𝛾
𝑥
𝑦
Euler-Gamma
𝛾
Euler-Gamma
𝛼
Euler-Gamma
𝛾
𝛼
superscript
subscript
0
1
superscript
𝑢
𝛼
1
superscript
1
𝑢
𝛾
𝛼
1
superscript
1
𝑢
𝑥
𝛽
superscript
1
𝑢
𝑦
superscript
𝛽
′
𝑢
{\displaystyle{\displaystyle{F_{1}}\left(\alpha;\beta,\beta^{\prime};\gamma;x,%
y\right)=\frac{\Gamma\left(\gamma\right)}{\Gamma\left(\alpha\right)\Gamma\left%
(\gamma-\alpha\right)}\int_{0}^{1}\frac{u^{\alpha-1}(1-u)^{\gamma-\alpha-1}}{(%
1-ux)^{\beta}(1-uy)^{\beta^{\prime}}}\mathrm{d}u,}}
ℜ
α
>
0
𝛼
0
{\displaystyle{\displaystyle\Re\alpha>0}}
ℜ
(
γ
-
α
)
>
0
𝛾
𝛼
0
{\displaystyle{\displaystyle\Re(\gamma-\alpha)>0}}
F
1
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α
;
β
,
β
′
;
γ
;
missing
,
missing
)
Appell-F-1
𝛼
𝛽
superscript
𝛽
′
𝛾
missing
missing
{\displaystyle{\displaystyle{F_{1}}\left(\NVar{\alpha};\NVar{\beta},\NVar{%
\beta^{\prime}};\NVar{\gamma};missing,missing\right)\)\@add@PDF@RDFa@triples\end{document}}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
∫
{\displaystyle{\displaystyle\int}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
Identifiers
