DLMF:17.10.E4 (Q5450)

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DLMF:17.10.E4
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    ψ 2 2 ( e , f a q / c , a q / d ; q , a q e f ) = ( q / c , q / d , a q / e , a q / f ; q ) ( a q , q / a , a q / ( c d ) , a q / ( e f ) ; q ) n = - ( 1 - a q 2 n ) ( c , d , e , f ; q ) n ( 1 - a ) ( a q / c , a q / d , a q / e , a q / f ; q ) n ( q a 3 c d e f ) n q n 2 . q-hypergeometric-rpsis 2 2 𝑒 𝑓 𝑎 𝑞 𝑐 𝑎 𝑞 𝑑 𝑞 𝑎 𝑞 𝑒 𝑓 q-multiple-Pochhammer 𝑞 𝑐 𝑞 𝑑 𝑎 𝑞 𝑒 𝑎 𝑞 𝑓 𝑞 q-multiple-Pochhammer 𝑎 𝑞 𝑞 𝑎 𝑎 𝑞 𝑐 𝑑 𝑎 𝑞 𝑒 𝑓 𝑞 superscript subscript 𝑛 1 𝑎 superscript 𝑞 2 𝑛 q-multiple-Pochhammer 𝑐 𝑑 𝑒 𝑓 𝑞 𝑛 1 𝑎 q-multiple-Pochhammer 𝑎 𝑞 𝑐 𝑎 𝑞 𝑑 𝑎 𝑞 𝑒 𝑎 𝑞 𝑓 𝑞 𝑛 superscript 𝑞 superscript 𝑎 3 𝑐 𝑑 𝑒 𝑓 𝑛 superscript 𝑞 superscript 𝑛 2 {\displaystyle{\displaystyle{{}_{2}\psi_{2}}\left({e,f\atop aq/c,aq/d};q,\frac% {aq}{ef}\right)=\frac{\left(q/c,q/d,aq/e,aq/f;q\right)_{\infty}}{\left(aq,q/a,% aq/(cd),aq/(ef);q\right)_{\infty}}\*\sum_{n=-\infty}^{\infty}\frac{(1-aq^{2n})% \left(c,d,e,f;q\right)_{n}}{(1-a)\left(aq/c,aq/d,aq/e,aq/f;q\right)_{n}}\left(% \frac{qa^{3}}{cdef}\right)^{n}q^{n^{2}}.}}
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    DLMF:17.10.E4
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    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)}}
    C17.S4.E3.m2acdec
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    ( 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}}}}
    C17.S2.SS1.p1.m6acdec
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    q 𝑞 {\displaystyle{\displaystyle q}}
    C17.S1.XMD10.m1cdec
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    n 𝑛 {\displaystyle{\displaystyle n}}
    C17.S1.XMD4.m1adec
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