DLMF:17.10.E3 (Q5449)

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DLMF:17.10.E3
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    Statements

    Defining formula
    ψ 8 8 ⁡ ( q ⁢ a 1 2 , - q ⁢ a 1 2 , c , d , e , f , a ⁢ q - n , q - n a 1 2 , - a 1 2 , a ⁢ q / c , a ⁢ q / d , a ⁢ q / e , a ⁢ q / f , q n + 1 , a ⁢ q n + 1 ; q , a 2 ⁢ q 2 ⁢ n + 2 c ⁢ d ⁢ e ⁢ f ) = ( a ⁢ q , q / a , a ⁢ q / ( c ⁢ d ) , a ⁢ q / ( e ⁢ f ) ; q ) n ( q / c , q / d , a ⁢ q / e , a ⁢ q / f ; q ) n ⁢ ψ 4 4 ⁡ ( e , f , a ⁢ q n + 1 / ( c ⁢ d ) , q - n a ⁢ q / c , a ⁢ q / d , q n + 1 , e ⁢ f / ( a ⁢ q n ) ; q , q ) , q-hypergeometric-rpsis 8 8 𝑞 superscript 𝑎 1 2 𝑞 superscript 𝑎 1 2 𝑐 𝑑 𝑒 𝑓 𝑎 superscript 𝑞 𝑛 superscript 𝑞 𝑛 superscript 𝑎 1 2 superscript 𝑎 1 2 𝑎 𝑞 𝑐 𝑎 𝑞 𝑑 𝑎 𝑞 𝑒 𝑎 𝑞 𝑓 superscript 𝑞 𝑛 1 𝑎 superscript 𝑞 𝑛 1 𝑞 superscript 𝑎 2 superscript 𝑞 2 𝑛 2 𝑐 𝑑 𝑒 𝑓 q-multiple-Pochhammer 𝑎 𝑞 𝑞 𝑎 𝑎 𝑞 𝑐 𝑑 𝑎 𝑞 𝑒 𝑓 𝑞 𝑛 q-multiple-Pochhammer 𝑞 𝑐 𝑞 𝑑 𝑎 𝑞 𝑒 𝑎 𝑞 𝑓 𝑞 𝑛 q-hypergeometric-rpsis 4 4 𝑒 𝑓 𝑎 superscript 𝑞 𝑛 1 𝑐 𝑑 superscript 𝑞 𝑛 𝑎 𝑞 𝑐 𝑎 𝑞 𝑑 superscript 𝑞 𝑛 1 𝑒 𝑓 𝑎 superscript 𝑞 𝑛 𝑞 𝑞 {\displaystyle{\displaystyle{{}_{8}\psi_{8}}\left({qa^{\frac{1}{2}},-qa^{\frac% {1}{2}},c,d,e,f,aq^{-n},q^{-n}\atop a^{\frac{1}{2}},-a^{\frac{1}{2}},aq/c,aq/d% ,aq/e,aq/f,q^{n+1},aq^{n+1}};q,\frac{a^{2}q^{2n+2}}{cdef}\right)=\frac{\left(% aq,q/a,aq/(cd),aq/(ef);q\right)_{n}}{\left(q/c,q/d,aq/e,aq/f;q\right)_{n}}\*{{% }_{4}\psi_{4}}\left({e,f,aq^{n+1}/(cd),q^{-n}\atop aq/c,aq/d,q^{n+1},ef/(aq^{n% })};q,q\right),}}
    0 references
    DLMF id
    DLMF:17.10.E3
    0 references
    Symbols used
    bilateral basic hypergeometric (or bilateral $$q$$ -hypergeometric) function
    Defining formula
    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)}}
    xml-id
    C17.S4.E3.m2abdec
    0 references
    Q11713
    Defining formula
    ( 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}}}}
    xml-id
    C17.S2.SS1.p1.m6abdec
    0 references
     
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