DLMF:17.9.E14 (Q5440)

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DLMF:17.9.E14
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    ϕ 3 4 ( q - n , a , b , c d , e , f ; q , q ) = ( e / a , f / a ; q ) n ( e , f ; q ) n a n ϕ 3 4 ( q - n , a , d / b , d / c d , a q 1 - n / e , a q 1 - n / f ; q , q ) = ( a , e f / ( a b ) , e f / ( a c ) ; q ) n ( e , f , e f / ( a b c ) ; q ) n ϕ 3 4 ( q - n , e / a , f / a , e f / ( a b c ) e f / ( a b ) , e f / ( a c ) , q 1 - n / a ; q , q ) . q-hypergeometric-rphis 4 3 superscript 𝑞 𝑛 𝑎 𝑏 𝑐 𝑑 𝑒 𝑓 𝑞 𝑞 q-multiple-Pochhammer 𝑒 𝑎 𝑓 𝑎 𝑞 𝑛 q-multiple-Pochhammer 𝑒 𝑓 𝑞 𝑛 superscript 𝑎 𝑛 q-hypergeometric-rphis 4 3 superscript 𝑞 𝑛 𝑎 𝑑 𝑏 𝑑 𝑐 𝑑 𝑎 superscript 𝑞 1 𝑛 𝑒 𝑎 superscript 𝑞 1 𝑛 𝑓 𝑞 𝑞 q-multiple-Pochhammer 𝑎 𝑒 𝑓 𝑎 𝑏 𝑒 𝑓 𝑎 𝑐 𝑞 𝑛 q-multiple-Pochhammer 𝑒 𝑓 𝑒 𝑓 𝑎 𝑏 𝑐 𝑞 𝑛 q-hypergeometric-rphis 4 3 superscript 𝑞 𝑛 𝑒 𝑎 𝑓 𝑎 𝑒 𝑓 𝑎 𝑏 𝑐 𝑒 𝑓 𝑎 𝑏 𝑒 𝑓 𝑎 𝑐 superscript 𝑞 1 𝑛 𝑎 𝑞 𝑞 {\displaystyle{\displaystyle{{}_{4}\phi_{3}}\left({q^{-n},a,b,c\atop d,e,f};q,% q\right)=\frac{\left(e/a,f/a;q\right)_{n}}{\left(e,f;q\right)_{n}}a^{n}{{}_{4}% \phi_{3}}\left({q^{-n},a,d/b,d/c\atop d,aq^{1-n}/e,aq^{1-n}/f};q,q\right)=% \frac{\left(a,ef/(ab),ef/(ac);q\right)_{n}}{\left(e,f,ef/(abc);q\right)_{n}}{{% }_{4}\phi_{3}}\left({q^{-n},e/a,f/a,ef/(abc)\atop ef/(ab),ef/(ac),q^{1-n}/a};q% ,q\right).}}
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