DLMF:17.6.E6 (Q5373)

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DLMF:17.6.E6
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    Statements

    Defining formula
    ϕ 1 2 ⁡ ( a , b c ; q , z ) = ( b , a ⁢ z ; q ) ∞ ( c , z ; q ) ∞ ⁢ ϕ 1 2 ⁡ ( c / b , z a ⁢ z ; q , b ) , q-hypergeometric-rphis 2 1 𝑎 𝑏 𝑐 𝑞 𝑧 q-multiple-Pochhammer 𝑏 𝑎 𝑧 𝑞 q-multiple-Pochhammer 𝑐 𝑧 𝑞 q-hypergeometric-rphis 2 1 𝑐 𝑏 𝑧 𝑎 𝑧 𝑞 𝑏 {\displaystyle{\displaystyle{{}_{2}\phi_{1}}\left({a,b\atop c};q,z\right)=% \frac{\left(b,az;q\right)_{\infty}}{\left(c,z;q\right)_{\infty}}{{}_{2}\phi_{1% }}\left({c/b,z\atop az};q,b\right),}}
    0 references
    DLMF id
    DLMF:17.6.E6
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    constraint
    | z | < 1 , | b | < 1 formulae-sequence 𝑧 1 𝑏 1 {\displaystyle{\displaystyle|z|<1,|b|<1}}
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    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
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    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.m6acdec
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    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1edec
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    Q11718
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C17.S1.XMD7.m1dec
    0 references
     
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