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DLMF:17.6.E14 - MaRDI portal
Statements
∑
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∞
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n
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z
n
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ϕ
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superscript
subscript
𝑛
0
q-Pochhammer-symbol
𝑎
𝑞
𝑛
q-Pochhammer-symbol
𝑏
superscript
𝑞
2
𝑛
superscript
𝑧
𝑛
q-Pochhammer-symbol
𝑞
𝑞
𝑛
q-Pochhammer-symbol
𝑎
𝑧
𝑏
superscript
𝑞
2
𝑛
q-multiple-Pochhammer
𝑎
𝑧
𝑏
𝑧
superscript
𝑞
2
q-multiple-Pochhammer
𝑧
𝑎
𝑧
𝑏
superscript
𝑞
2
q-hypergeometric-rphis
2
1
𝑎
𝑏
𝑏
𝑧
superscript
𝑞
2
𝑧
𝑞
{\displaystyle{\displaystyle\sum_{n=0}^{\infty}\frac{\left(a;q\right)_{n}\left%
(b;q^{2}\right)_{n}z^{n}}{\left(q;q\right)_{n}\left(azb;q^{2}\right)_{n}}=%
\frac{\left(az,bz;q^{2}\right)_{\infty}}{\left(z,azb;q^{2}\right)_{\infty}}{{}%
_{2}\phi_{1}}\left({a,b\atop bz};q^{2},zq\right).}}
(
a
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q
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n
q-Pochhammer-symbol
𝑎
𝑞
𝑛
{\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}
ϕ
s
r
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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)}}
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n
q-multiple-Pochhammer
subscript
𝑎
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subscript
𝑎
2
…
subscript
𝑎
𝑟
𝑞
𝑛
{\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}%
\right)_{\NVar{n}}}}
q
𝑞
{\displaystyle{\displaystyle q}}
n
𝑛
{\displaystyle{\displaystyle n}}
z
𝑧
{\displaystyle{\displaystyle z}}
Identifiers