DLMF:17.8.E7 (Q5426)

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DLMF:17.8.E7
No description defined

    Statements

    Defining formula
    ψ 6 6 ⁡ ( q ⁢ a 1 2 , - q ⁢ a 1 2 , b , c , d , e a 1 2 , - a 1 2 , a ⁢ q / b , a ⁢ q / c , a ⁢ q / d , a ⁢ q / e ; q , q ⁢ a 2 b ⁢ c ⁢ d ⁢ e ) = ( a ⁢ q , a ⁢ q / ( b ⁢ c ) , a ⁢ q / ( b ⁢ d ) , a ⁢ q / ( b ⁢ e ) , a ⁢ q / ( c ⁢ d ) , a ⁢ q / ( c ⁢ e ) , a ⁢ q / ( d ⁢ e ) , q , q / a ; q ) ∞ ( a ⁢ q / b , a ⁢ q / c , a ⁢ q / d , a ⁢ q / e , q / b , q / c , q / d , q / e , q ⁢ a 2 / ( b ⁢ c ⁢ d ⁢ e ) ; q ) ∞ . q-hypergeometric-rpsis 6 6 𝑞 superscript 𝑎 1 2 𝑞 superscript 𝑎 1 2 𝑏 𝑐 𝑑 𝑒 superscript 𝑎 1 2 superscript 𝑎 1 2 𝑎 𝑞 𝑏 𝑎 𝑞 𝑐 𝑎 𝑞 𝑑 𝑎 𝑞 𝑒 𝑞 𝑞 superscript 𝑎 2 𝑏 𝑐 𝑑 𝑒 q-multiple-Pochhammer 𝑎 𝑞 𝑎 𝑞 𝑏 𝑐 𝑎 𝑞 𝑏 𝑑 𝑎 𝑞 𝑏 𝑒 𝑎 𝑞 𝑐 𝑑 𝑎 𝑞 𝑐 𝑒 𝑎 𝑞 𝑑 𝑒 𝑞 𝑞 𝑎 𝑞 q-multiple-Pochhammer 𝑎 𝑞 𝑏 𝑎 𝑞 𝑐 𝑎 𝑞 𝑑 𝑎 𝑞 𝑒 𝑞 𝑏 𝑞 𝑐 𝑞 𝑑 𝑞 𝑒 𝑞 superscript 𝑎 2 𝑏 𝑐 𝑑 𝑒 𝑞 {\displaystyle{\displaystyle{{}_{6}\psi_{6}}\left({qa^{\frac{1}{2}},-qa^{\frac% {1}{2}},b,c,d,e\atop a^{\frac{1}{2}},-a^{\frac{1}{2}},aq/b,aq/c,aq/d,aq/e};q,% \frac{qa^{2}}{bcde}\right)=\frac{\left(aq,aq/(bc),aq/(bd),aq/(be),aq/(cd),aq/(% ce),aq/(de),q,q/a;q\right)_{\infty}}{\left(aq/b,aq/c,aq/d,aq/e,q/b,q/c,q/d,q/e% ,qa^{2}/(bcde);q\right)_{\infty}}.}}
    0 references
    DLMF id
    DLMF:17.8.E7
    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.m2addec
    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.m6afdec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1fdec
    0 references
     
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