DLMF:17.7.E7 (Q5403)

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DLMF:17.7.E7
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    Statements

    Defining formula
    ϕ 3 4 ⁡ ( a , - q ⁢ a 1 2 , b , c - a 1 2 , a ⁢ q / b , a ⁢ q / c ; q , q ⁢ a 1 2 b ⁢ c ) = ( a ⁢ q , q ⁢ a 1 2 / b , q ⁢ a 1 2 / c , a ⁢ q / ( b ⁢ c ) ; q ) ∞ ( a ⁢ q / b , a ⁢ q / c , q ⁢ a 1 2 , q ⁢ a 1 2 / ( b ⁢ c ) ; q ) ∞ . q-hypergeometric-rphis 4 3 𝑎 𝑞 superscript 𝑎 1 2 𝑏 𝑐 superscript 𝑎 1 2 𝑎 𝑞 𝑏 𝑎 𝑞 𝑐 𝑞 𝑞 superscript 𝑎 1 2 𝑏 𝑐 q-multiple-Pochhammer 𝑎 𝑞 𝑞 superscript 𝑎 1 2 𝑏 𝑞 superscript 𝑎 1 2 𝑐 𝑎 𝑞 𝑏 𝑐 𝑞 q-multiple-Pochhammer 𝑎 𝑞 𝑏 𝑎 𝑞 𝑐 𝑞 superscript 𝑎 1 2 𝑞 superscript 𝑎 1 2 𝑏 𝑐 𝑞 {\displaystyle{\displaystyle{{}_{4}\phi_{3}}\left({a,-qa^{\frac{1}{2}},b,c% \atop-a^{\frac{1}{2}},aq/b,aq/c};q,\frac{qa^{\frac{1}{2}}}{bc}\right)=\frac{% \left(aq,qa^{\frac{1}{2}}/b,qa^{\frac{1}{2}}/c,aq/(bc);q\right)_{\infty}}{% \left(aq/b,aq/c,qa^{\frac{1}{2}},qa^{\frac{1}{2}}/(bc);q\right)_{\infty}}.}}
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    DLMF id
    DLMF:17.7.E7
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