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Statements
ϕ
1
2
(
q
α
,
q
β
q
γ
;
q
,
z
)
=
Γ
q
(
γ
)
Γ
q
(
β
)
Γ
q
(
γ
-
β
)
∫
0
1
t
β
-
1
(
t
q
;
q
)
γ
-
β
-
1
(
x
t
;
q
)
α
d
q
t
.
q-hypergeometric-rphis
2
1
superscript
𝑞
𝛼
superscript
𝑞
𝛽
superscript
𝑞
𝛾
𝑞
𝑧
q-Gamma
𝑞
𝛾
q-Gamma
𝑞
𝛽
q-Gamma
𝑞
𝛾
𝛽
superscript
subscript
0
1
superscript
𝑡
𝛽
1
q-Pochhammer-symbol
𝑡
𝑞
𝑞
𝛾
𝛽
1
q-Pochhammer-symbol
𝑥
𝑡
𝑞
𝛼
q-differential
𝑞
𝑡
{\displaystyle{\displaystyle{{}_{2}\phi_{1}}\left({q^{\alpha},q^{\beta}\atop q%
^{\gamma}};q,z\right)=\frac{\Gamma_{q}\left(\gamma\right)}{\Gamma_{q}\left(%
\beta\right)\Gamma_{q}\left(\gamma-\beta\right)}\int_{0}^{1}\frac{t^{\beta-1}%
\left(tq;q\right)_{\gamma-\beta-1}}{\left(xt;q\right)_{\alpha}}{\mathrm{d}}_{q%
}t.}}
∫
{\displaystyle{\displaystyle\int}}
Γ
q
(
z
)
q-Gamma
𝑞
𝑧
{\displaystyle{\displaystyle\Gamma_{\NVar{q}}\left(\NVar{z}\right)}}
(
a
;
q
)
n
q-Pochhammer-symbol
𝑎
𝑞
𝑛
{\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}
d
q
x
q-differential
𝑞
𝑥
{\displaystyle{\displaystyle{\mathrm{d}}_{\NVar{q}}\NVar{x}}}
ϕ
s
r
+
1
(
a
0
,
…
,
a
r
;
b
1
,
…
,
b
s
;
q
,
z
)
q-hypergeometric-rphis
𝑟
1
𝑠
subscript
𝑎
0
…
subscript
𝑎
𝑟
subscript
𝑏
1
…
subscript
𝑏
𝑠
𝑞
𝑧
{\displaystyle{\displaystyle{{}_{\NVar{r+1}}\phi_{\NVar{s}}}\left(\NVar{a_{0},%
\dots,a_{r}};\NVar{b_{1},\dots,b_{s}};\NVar{q},\NVar{z}\right)}}
q
𝑞
{\displaystyle{\displaystyle q}}
z
𝑧
{\displaystyle{\displaystyle z}}
x
𝑥
{\displaystyle{\displaystyle x}}
Identifiers
