DLMF:17.6.E15 (Q5382)

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DLMF:17.6.E15
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    Statements

    Defining formula
    ϕ 1 2 ⁡ ( a , b c ; q , z ) = ( a ⁢ b ⁢ z / c , q / c ; q ) ∞ ( a ⁢ z / c , q / a ; q ) ∞ ⁢ ϕ 1 2 ⁡ ( c / a , c ⁢ q / ( a ⁢ b ⁢ z ) c ⁢ q / ( a ⁢ z ) ; q , b ⁢ q / c ) - ( b , q / c , c / a , a ⁢ z / q , q 2 / ( a ⁢ z ) ; q ) ∞ ( c / q , b ⁢ q / c , q / a , a ⁢ z / c , c ⁢ q / ( a ⁢ z ) ; q ) ∞ ⁢ ϕ 1 2 ⁡ ( a ⁢ q / c , b ⁢ q / c q 2 / c ; q , z ) , q-hypergeometric-rphis 2 1 𝑎 𝑏 𝑐 𝑞 𝑧 q-multiple-Pochhammer 𝑎 𝑏 𝑧 𝑐 𝑞 𝑐 𝑞 q-multiple-Pochhammer 𝑎 𝑧 𝑐 𝑞 𝑎 𝑞 q-hypergeometric-rphis 2 1 𝑐 𝑎 𝑐 𝑞 𝑎 𝑏 𝑧 𝑐 𝑞 𝑎 𝑧 𝑞 𝑏 𝑞 𝑐 q-multiple-Pochhammer 𝑏 𝑞 𝑐 𝑐 𝑎 𝑎 𝑧 𝑞 superscript 𝑞 2 𝑎 𝑧 𝑞 q-multiple-Pochhammer 𝑐 𝑞 𝑏 𝑞 𝑐 𝑞 𝑎 𝑎 𝑧 𝑐 𝑐 𝑞 𝑎 𝑧 𝑞 q-hypergeometric-rphis 2 1 𝑎 𝑞 𝑐 𝑏 𝑞 𝑐 superscript 𝑞 2 𝑐 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{2}\phi_{1}}\left({a,b\atop c};q,z\right)=% \frac{\left(abz/c,q/c;q\right)_{\infty}}{\left(az/c,q/a;q\right)_{\infty}}{{}_% {2}\phi_{1}}\left({c/a,cq/(abz)\atop cq/(az)};q,bq/c\right)-\frac{\left(b,q/c,% c/a,az/q,q^{2}/(az);q\right)_{\infty}}{\left(c/q,bq/c,q/a,az/c,cq/(az);q\right% )_{\infty}}{{}_{2}\phi_{1}}\left({aq/c,bq/c\atop q^{2}/c};q,z\right),}}
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    DLMF id
    DLMF:17.6.E15
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    constraint
    | z | < 1 , | b ⁢ q | < | c | formulae-sequence 𝑧 1 𝑏 𝑞 𝑐 {\displaystyle{\displaystyle|z|<1,|bq|<|c|}}
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