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Statements
F
1
2
(
α
,
β
;
γ
;
z
)
=
H
ℓ
(
1
,
α
β
;
α
,
β
,
γ
,
δ
;
z
)
=
H
ℓ
(
0
,
0
;
α
,
β
,
γ
,
α
+
β
+
1
-
γ
;
z
)
=
H
ℓ
(
a
,
a
α
β
;
α
,
β
,
γ
,
α
+
β
+
1
-
γ
;
z
)
.
Gauss-hypergeometric-F-as-2F1
𝛼
𝛽
𝛾
𝑧
Heun-local
1
𝛼
𝛽
𝛼
𝛽
𝛾
𝛿
𝑧
Heun-local
0
0
𝛼
𝛽
𝛾
𝛼
𝛽
1
𝛾
𝑧
Heun-local
𝑎
𝑎
𝛼
𝛽
𝛼
𝛽
𝛾
𝛼
𝛽
1
𝛾
𝑧
{\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\alpha,\beta;\gamma;z\right)=%
\mathit{H\!\ell}\left(1,\alpha\beta;\alpha,\beta,\gamma,\delta;z\right)=%
\mathit{H\!\ell}\left(0,0;\alpha,\beta,\gamma,\alpha+\beta+1-\gamma;z\right)=%
\mathit{H\!\ell}\left(a,a\alpha\beta;\alpha,\beta,\gamma,\alpha+\beta+1-\gamma%
;z\right).}}
F
1
2
(
a
,
b
;
c
;
z
)
Gauss-hypergeometric-F-as-2F1
𝑎
𝑏
𝑐
𝑧
{\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};%
\NVar{z}\right)}}
H
ℓ
(
a
,
q
;
α
,
β
,
γ
,
missing
;
missing
)
Heun-local
𝑎
𝑞
𝛼
𝛽
𝛾
missing
missing
{\displaystyle{\displaystyle\mathit{H\!\ell}\left(\NVar{a},\NVar{q};\NVar{%
\alpha},\NVar{\beta},\NVar{\gamma},\NVar{missing};missing\right)\)\@add@PDF@RDFa@triples\end{document}}}
z
𝑧
{\displaystyle{\displaystyle z}}
γ
𝛾
{\displaystyle{\displaystyle\gamma}}
δ
𝛿
{\displaystyle{\displaystyle\delta}}
a
𝑎
{\displaystyle{\displaystyle a}}
α
𝛼
{\displaystyle{\displaystyle\alpha}}
β
𝛽
{\displaystyle{\displaystyle\beta}}
