DLMF:17.9.E6 (Q5432)

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DLMF:17.9.E6
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    Statements

    Defining formula
    ϕ 2 3 ⁡ ( a , b , c d , e ; q , d ⁢ e / ( a ⁢ b ⁢ c ) ) = ( e / a , d ⁢ e / ( b ⁢ c ) ; q ) ∞ ( e , d ⁢ e / ( a ⁢ b ⁢ c ) ; q ) ∞ ⁢ ϕ 2 3 ⁡ ( a , d / b , d / c d , d ⁢ e / ( b ⁢ c ) ; q , e / a ) , q-hypergeometric-rphis 3 2 𝑎 𝑏 𝑐 𝑑 𝑒 𝑞 𝑑 𝑒 𝑎 𝑏 𝑐 q-multiple-Pochhammer 𝑒 𝑎 𝑑 𝑒 𝑏 𝑐 𝑞 q-multiple-Pochhammer 𝑒 𝑑 𝑒 𝑎 𝑏 𝑐 𝑞 q-hypergeometric-rphis 3 2 𝑎 𝑑 𝑏 𝑑 𝑐 𝑑 𝑑 𝑒 𝑏 𝑐 𝑞 𝑒 𝑎 {\displaystyle{\displaystyle{{}_{3}\phi_{2}}\left({a,b,c\atop d,e};q,de/(abc)% \right)=\frac{\left(e/a,de/(bc);q\right)_{\infty}}{\left(e,de/(abc);q\right)_{% \infty}}{{}_{3}\phi_{2}}\left({a,d/b,d/c\atop d,de/(bc)};q,e/a\right),}}
    0 references
    DLMF id
    DLMF:17.9.E6
    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.m2aedec
    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.m6aadec
    0 references
     
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