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Statements
H
ℓ
(
1
2
+
i
3
2
,
α
β
(
1
2
+
i
3
6
)
;
α
,
β
,
1
3
(
α
+
β
+
1
)
,
1
3
(
α
+
β
+
1
)
;
z
)
=
F
1
2
(
1
3
α
,
1
3
β
;
1
3
(
α
+
β
+
1
)
;
1
-
(
1
-
(
3
2
-
i
3
2
)
z
)
3
)
.
Heun-local
1
2
𝑖
3
2
𝛼
𝛽
1
2
𝑖
3
6
𝛼
𝛽
1
3
𝛼
𝛽
1
1
3
𝛼
𝛽
1
𝑧
Gauss-hypergeometric-F-as-2F1
1
3
𝛼
1
3
𝛽
1
3
𝛼
𝛽
1
1
superscript
1
3
2
𝑖
3
2
𝑧
3
{\displaystyle{\displaystyle\mathit{H\!\ell}\left(\tfrac{1}{2}+i\tfrac{\sqrt{3%
}}{2},\alpha\beta(\tfrac{1}{2}+i\tfrac{\sqrt{3}}{6});\alpha,\beta,\tfrac{1}{3}%
(\alpha+\beta+1),\tfrac{1}{3}(\alpha+\beta+1);z\right)={{}_{2}F_{1}}\left(%
\tfrac{1}{3}\alpha,\tfrac{1}{3}\beta;\tfrac{1}{3}(\alpha+\beta+1);1-\left(1-%
\left(\tfrac{3}{2}-i\tfrac{\sqrt{3}}{2}\right)z\right)^{3}\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}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
z
𝑧
{\displaystyle{\displaystyle z}}
α
𝛼
{\displaystyle{\displaystyle\alpha}}
β
𝛽
{\displaystyle{\displaystyle\beta}}
