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Statements
Q
n
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cos
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=
p
n
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cos
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n
∑
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0
n
q
ℓ
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ℓ
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q
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n
-
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n
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ℓ
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q
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ℓ
∏
j
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1
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a
q
j
cos
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a
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=
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n
a
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ϕ
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3
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q
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e
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θ
a
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0
;
q
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q
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(
b
e
-
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θ
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n
e
i
n
θ
ϕ
1
2
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q
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e
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-
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e
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q
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AlSalam-Chihara-polynomial-Q
𝑛
𝜃
𝑎
𝑏
𝑞
Askey-Wilson-polynomial-p
𝑛
𝜃
𝑎
𝑏
0
0
𝑞
superscript
𝑎
𝑛
superscript
subscript
ℓ
0
𝑛
superscript
𝑞
ℓ
q-Pochhammer-symbol
𝑎
𝑏
superscript
𝑞
ℓ
𝑞
𝑛
ℓ
q-Pochhammer-symbol
superscript
𝑞
𝑛
𝑞
ℓ
q-Pochhammer-symbol
𝑞
𝑞
ℓ
superscript
subscript
product
𝑗
0
ℓ
1
1
2
𝑎
superscript
𝑞
𝑗
𝜃
superscript
𝑎
2
superscript
𝑞
2
𝑗
q-Pochhammer-symbol
𝑎
𝑏
𝑞
𝑛
superscript
𝑎
𝑛
q-hypergeometric-rphis
3
2
superscript
𝑞
𝑛
𝑎
superscript
𝑒
imaginary-unit
𝜃
𝑎
superscript
𝑒
imaginary-unit
𝜃
𝑎
𝑏
0
𝑞
𝑞
q-Pochhammer-symbol
𝑏
superscript
𝑒
imaginary-unit
𝜃
𝑞
𝑛
superscript
𝑒
imaginary-unit
𝑛
𝜃
q-hypergeometric-rphis
2
1
superscript
𝑞
𝑛
𝑎
superscript
𝑒
imaginary-unit
𝜃
superscript
𝑏
1
superscript
𝑞
1
𝑛
superscript
𝑒
imaginary-unit
𝜃
𝑞
superscript
𝑏
1
𝑞
superscript
𝑒
imaginary-unit
𝜃
{\displaystyle{\displaystyle Q_{n}\left(\cos\theta;a,b\,|\,q\right)=p_{n}\left%
(\cos\theta;a,b,0,0\,|\,q\right)=a^{-n}\sum_{\ell=0}^{n}q^{\ell}\frac{\left(%
abq^{\ell};q\right)_{n-\ell}\left(q^{-n};q\right)_{\ell}}{\left(q;q\right)_{%
\ell}}\*\prod_{j=0}^{\ell-1}(1-2aq^{j}\cos\theta+a^{2}q^{2j})=\frac{\left(ab;q%
\right)_{n}}{a^{n}}{{}_{3}\phi_{2}}\left({q^{-n},ae^{\mathrm{i}\theta},ae^{-%
\mathrm{i}\theta}\atop ab,0};q,q\right)=\left(be^{-\mathrm{i}\theta};q\right)_%
{n}e^{\mathrm{i}n\theta}{{}_{2}\phi_{1}}\left({q^{-n},ae^{\mathrm{i}\theta}%
\atop b^{-1}q^{1-n}e^{\mathrm{i}\theta}};q,b^{-1}qe^{-\mathrm{i}\theta}\right)%
.}}
p
n
(
x
;
a
,
b
,
c
,
d
|
missing
)
Askey-Wilson-polynomial-p
𝑛
𝑥
𝑎
𝑏
𝑐
𝑑
missing
{\displaystyle{\displaystyle p_{\NVar{n}}\left(\NVar{x};\NVar{a},\NVar{b},%
\NVar{c},\NVar{d}\,|\,missing\right)\)\@add@PDF@RDFa@triples\end{document}}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
(
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)}}
q
𝑞
{\displaystyle{\displaystyle q}}
ℓ
ℓ
{\displaystyle{\displaystyle\ell}}
n
𝑛
{\displaystyle{\displaystyle n}}
x
𝑥
{\displaystyle{\displaystyle x}}
Identifiers
