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Statements
Q
n
(
1
2
(
a
q
-
y
+
a
-
1
q
y
)
;
a
,
b
|
q
-
1
)
=
(
-
1
)
n
b
n
q
-
1
2
n
(
n
-
1
)
(
(
a
b
)
-
1
;
q
)
n
ϕ
1
3
(
q
-
n
,
q
-
y
,
a
-
2
q
y
(
a
b
)
-
1
;
q
,
q
n
a
b
-
1
)
.
q-inverse-AlSalam-Chihara-polynomial-Q
𝑛
1
2
𝑎
superscript
𝑞
𝑦
superscript
𝑎
1
superscript
𝑞
𝑦
𝑎
𝑏
superscript
𝑞
1
superscript
1
𝑛
superscript
𝑏
𝑛
superscript
𝑞
1
2
𝑛
𝑛
1
q-Pochhammer-symbol
superscript
𝑎
𝑏
1
𝑞
𝑛
q-hypergeometric-rphis
3
1
superscript
𝑞
𝑛
superscript
𝑞
𝑦
superscript
𝑎
2
superscript
𝑞
𝑦
superscript
𝑎
𝑏
1
𝑞
superscript
𝑞
𝑛
𝑎
superscript
𝑏
1
{\displaystyle{\displaystyle Q_{n}\left(\tfrac{1}{2}(aq^{-y}+a^{-1}q^{y});a,b%
\,|\,q^{-1}\right)=(-1)^{n}b^{n}q^{-\frac{1}{2}n(n-1)}\*\left((ab)^{-1};q%
\right)_{n}{{}_{3}\phi_{1}}\left({q^{-n},q^{-y},a^{-2}q^{y}\atop(ab)^{-1}};q,q%
^{n}ab^{-1}\right).}}
(
a
;
q
)
n
q-Pochhammer-symbol
𝑎
𝑞
𝑛
{\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}
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)}}
y
𝑦
{\displaystyle{\displaystyle y}}
q
𝑞
{\displaystyle{\displaystyle q}}
n
𝑛
{\displaystyle{\displaystyle n}}
x
𝑥
{\displaystyle{\displaystyle x}}
