DLMF:17.7.E10 (Q5406)

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DLMF:17.7.E10
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    Statements

    Defining formula
    ϕ 7 8 ⁡ ( - c , q ⁢ ( - c ) 1 2 , - q ⁢ ( - c ) 1 2 , a , q / a , c , - d , - q / d ( - c ) 1 2 , - ( - c ) 1 2 , - c ⁢ q / a , - a ⁢ c , - q , c ⁢ q / d , c ⁢ d ; q , c ) = ( - c , - c ⁢ q ; q ) ∞ ⁢ ( a ⁢ c ⁢ d , a ⁢ c ⁢ q / d , c ⁢ d ⁢ q / a , c ⁢ q 2 / ( a ⁢ d ) ; q 2 ) ∞ ( c ⁢ d , c ⁢ q / d , - a ⁢ c , - c ⁢ q / a ; q ) ∞ . q-hypergeometric-rphis 8 7 𝑐 𝑞 superscript 𝑐 1 2 𝑞 superscript 𝑐 1 2 𝑎 𝑞 𝑎 𝑐 𝑑 𝑞 𝑑 superscript 𝑐 1 2 superscript 𝑐 1 2 𝑐 𝑞 𝑎 𝑎 𝑐 𝑞 𝑐 𝑞 𝑑 𝑐 𝑑 𝑞 𝑐 q-multiple-Pochhammer 𝑐 𝑐 𝑞 𝑞 q-multiple-Pochhammer 𝑎 𝑐 𝑑 𝑎 𝑐 𝑞 𝑑 𝑐 𝑑 𝑞 𝑎 𝑐 superscript 𝑞 2 𝑎 𝑑 superscript 𝑞 2 q-multiple-Pochhammer 𝑐 𝑑 𝑐 𝑞 𝑑 𝑎 𝑐 𝑐 𝑞 𝑎 𝑞 {\displaystyle{\displaystyle{{}_{8}\phi_{7}}\left({-c,q(-c)^{\frac{1}{2}},-q(-% c)^{\frac{1}{2}},a,q/a,c,-d,-q/d\atop(-c)^{\frac{1}{2}},-(-c)^{\frac{1}{2}},-% cq/a,-ac,-q,cq/d,cd};q,c\right)=\frac{\left(-c,-cq;q\right)_{\infty}\left(acd,% acq/d,cdq/a,cq^{2}/(ad);q^{2}\right)_{\infty}}{\left(cd,cq/d,-ac,-cq/a;q\right% )_{\infty}}.}}
    0 references
    DLMF id
    DLMF:17.7.E10
    0 references
    Symbols used
    basic hypergeometric (or $$q$$ -hypergeometric) function
    Defining formula
    ϕ s r + 1 ⁡ ( a 0 , … , a r ; b 1 , … , b s ; q , z ) 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)}}
    xml-id
    C17.S4.E1.m2aidec
    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.m6aidec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1idec
    0 references
     
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