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Statements
R
n
(
x
)
=
R
n
(
x
;
α
,
β
,
γ
,
δ
|
q
)
=
∑
ℓ
=
0
n
q
ℓ
(
q
-
n
,
α
β
q
n
+
1
;
q
)
ℓ
(
α
q
,
β
δ
q
,
γ
q
,
q
;
q
)
ℓ
∏
j
=
0
ℓ
-
1
(
1
-
q
j
x
+
γ
δ
q
2
j
+
1
)
=
ϕ
3
4
(
q
-
n
,
α
β
q
n
+
1
,
q
-
y
,
γ
δ
q
y
+
1
α
q
,
β
δ
q
,
γ
q
;
q
,
q
)
,
subscript
𝑅
𝑛
𝑥
q-Racah-polynomial-R
𝑛
𝑥
𝛼
𝛽
𝛾
𝛿
𝑞
superscript
subscript
ℓ
0
𝑛
superscript
𝑞
ℓ
q-multiple-Pochhammer
superscript
𝑞
𝑛
𝛼
𝛽
superscript
𝑞
𝑛
1
𝑞
ℓ
q-multiple-Pochhammer
𝛼
𝑞
𝛽
𝛿
𝑞
𝛾
𝑞
𝑞
𝑞
ℓ
superscript
subscript
product
𝑗
0
ℓ
1
1
superscript
𝑞
𝑗
𝑥
𝛾
𝛿
superscript
𝑞
2
𝑗
1
q-hypergeometric-rphis
4
3
superscript
𝑞
𝑛
𝛼
𝛽
superscript
𝑞
𝑛
1
superscript
𝑞
𝑦
𝛾
𝛿
superscript
𝑞
𝑦
1
𝛼
𝑞
𝛽
𝛿
𝑞
𝛾
𝑞
𝑞
𝑞
{\displaystyle{\displaystyle R_{n}(x)=R_{n}\left(x;\alpha,\beta,\gamma,\delta%
\,|\,q\right)=\sum_{\ell=0}^{n}\frac{q^{\ell}\left(q^{-n},\alpha\beta q^{n+1};%
q\right)_{\ell}}{\left(\alpha q,\beta\delta q,\gamma q,q;q\right)_{\ell}}\*%
\prod_{j=0}^{\ell-1}(1-q^{j}x+\gamma\delta q^{2j+1})={{}_{4}\phi_{3}}\left({q^%
{-n},\alpha\beta q^{n+1},q^{-y},\gamma\delta q^{y+1}\atop\alpha q,\beta\delta q%
,\gamma q};q,q\right),}}
n
=
0
,
1
,
…
,
N
𝑛
0
1
…
𝑁
{\displaystyle{\displaystyle n=0,1,\dots,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)}}
(
a
1
,
a
2
,
…
,
a
r
;
q
)
n
q-multiple-Pochhammer
subscript
𝑎
1
subscript
𝑎
2
…
subscript
𝑎
𝑟
𝑞
𝑛
{\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}%
\right)_{\NVar{n}}}}
y
𝑦
{\displaystyle{\displaystyle y}}
q
𝑞
{\displaystyle{\displaystyle q}}
ℓ
ℓ
{\displaystyle{\displaystyle\ell}}
n
𝑛
{\displaystyle{\displaystyle n}}
N
𝑁
{\displaystyle{\displaystyle N}}
δ
𝛿
{\displaystyle{\displaystyle\delta}}
x
𝑥
{\displaystyle{\displaystyle x}}
Identifiers
