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Statements
lim
q
→
1
-
ψ
r
r
(
q
a
1
,
q
a
2
,
…
,
q
a
r
q
b
1
,
q
b
2
,
…
,
q
b
r
;
q
,
z
)
=
H
r
r
(
a
1
,
a
2
,
…
,
a
r
b
1
,
b
2
,
…
,
b
r
;
z
)
.
subscript
→
𝑞
limit-from
1
q-hypergeometric-rpsis
𝑟
𝑟
superscript
𝑞
subscript
𝑎
1
superscript
𝑞
subscript
𝑎
2
…
superscript
𝑞
subscript
𝑎
𝑟
superscript
𝑞
subscript
𝑏
1
superscript
𝑞
subscript
𝑏
2
…
superscript
𝑞
subscript
𝑏
𝑟
𝑞
𝑧
hypergeometric-pHq
𝑟
𝑟
subscript
𝑎
1
subscript
𝑎
2
…
subscript
𝑎
𝑟
subscript
𝑏
1
subscript
𝑏
2
…
subscript
𝑏
𝑟
𝑧
{\displaystyle{\displaystyle\lim_{q\to 1-}{{}_{r}\psi_{r}}\left({q^{a_{1}},q^{%
a_{2}},\dots,q^{a_{r}}\atop q^{b_{1}},q^{b_{2}},\dots,q^{b_{r}}};q,z\right)={{%
}_{r}H_{r}}\left({a_{1},a_{2},\dots,a_{r}\atop b_{1},b_{2},\dots,b_{r}};z%
\right).}}
H
q
p
(
a
1
,
…
,
a
p
b
1
,
…
,
b
q
;
z
)
hypergeometric-pHq
𝑝
𝑞
subscript
𝑎
1
…
subscript
𝑎
𝑝
subscript
𝑏
1
…
subscript
𝑏
𝑞
𝑧
{\displaystyle{\displaystyle{{}_{\NVar{p}}H_{\NVar{q}}}\left({\NVar{a_{1},%
\dots,a_{p}}\atop\NVar{b_{1},\dots,b_{q}}};\NVar{z}\right)}}
ψ
s
r
(
a
1
,
…
,
a
r
;
b
1
,
…
,
b
s
;
q
,
z
)
q-hypergeometric-rpsis
𝑟
𝑠
subscript
𝑎
1
…
subscript
𝑎
𝑟
subscript
𝑏
1
…
subscript
𝑏
𝑠
𝑞
𝑧
{\displaystyle{\displaystyle{{}_{\NVar{r}}\psi_{\NVar{s}}}\left(\NVar{a_{1},%
\dots,a_{r}};\NVar{b_{1},\dots,b_{s}};\NVar{q},\NVar{z}\right)}}
q
𝑞
{\displaystyle{\displaystyle q}}
r
𝑟
{\displaystyle{\displaystyle r}}
z
𝑧
{\displaystyle{\displaystyle z}}
Identifiers
