DLMF:17.9.E17 (Q5443)

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DLMF:17.9.E17
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    Statements

    Defining formula
    ϕ 2 3 ⁡ ( a , b , c a ⁢ q / b , a ⁢ q / c ; q , a ⁢ q ⁢ z b ⁢ c ) = ( a ⁢ z ; q ) ∞ ( z ; q ) ∞ ⁢ ϕ 4 5 ⁡ ( a 1 2 , - a 1 2 , ( a ⁢ q ) 1 2 , - ( a ⁢ q ) 1 2 , a ⁢ q / ( b ⁢ c ) a ⁢ q / b , a ⁢ q / c , a ⁢ z , q / z ; q , q ) . q-hypergeometric-rphis 3 2 𝑎 𝑏 𝑐 𝑎 𝑞 𝑏 𝑎 𝑞 𝑐 𝑞 𝑎 𝑞 𝑧 𝑏 𝑐 q-Pochhammer-symbol 𝑎 𝑧 𝑞 q-Pochhammer-symbol 𝑧 𝑞 q-hypergeometric-rphis 5 4 superscript 𝑎 1 2 superscript 𝑎 1 2 superscript 𝑎 𝑞 1 2 superscript 𝑎 𝑞 1 2 𝑎 𝑞 𝑏 𝑐 𝑎 𝑞 𝑏 𝑎 𝑞 𝑐 𝑎 𝑧 𝑞 𝑧 𝑞 𝑞 {\displaystyle{\displaystyle{{}_{3}\phi_{2}}\left({a,b,c\atop aq/b,aq/c};q,% \frac{aqz}{bc}\right)=\frac{\left(az;q\right)_{\infty}}{\left(z;q\right)_{% \infty}}\*{{}_{5}\phi_{4}}\left({a^{\frac{1}{2}},-a^{\frac{1}{2}},(aq)^{\frac{% 1}{2}},-(aq)^{\frac{1}{2}},aq/(bc)\atop aq/b,aq/c,az,q/z};q,q\right).}}
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    DLMF id
    DLMF:17.9.E17
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