DLMF:17.6.E26 (Q5393)

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DLMF:17.6.E26
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    Statements

    test
    𝒟 q n ⁢ ( ( z ; q ) ∞ ( a ⁢ b ⁢ z / c ; q ) ∞ ⁢ ϕ 1 2 ⁡ ( a , b c ; q , z ) ) = ( c / a , c / b ; q ) n ( c ; q ) n ⁢ ( 1 - q ) n ⁢ ( a ⁢ b c ) n ⁢ ( z ⁢ q n ; q ) ∞ ( a ⁢ b ⁢ z / c ; q ) ∞ ⁢ ϕ 1 2 ⁡ ( a , b c ⁢ q n ; q , z ⁢ q n ) . superscript subscript 𝒟 𝑞 𝑛 q-Pochhammer-symbol 𝑧 𝑞 q-Pochhammer-symbol 𝑎 𝑏 𝑧 𝑐 𝑞 q-hypergeometric-rphis 2 1 𝑎 𝑏 𝑐 𝑞 𝑧 q-multiple-Pochhammer 𝑐 𝑎 𝑐 𝑏 𝑞 𝑛 q-Pochhammer-symbol 𝑐 𝑞 𝑛 superscript 1 𝑞 𝑛 superscript 𝑎 𝑏 𝑐 𝑛 q-Pochhammer-symbol 𝑧 superscript 𝑞 𝑛 𝑞 q-Pochhammer-symbol 𝑎 𝑏 𝑧 𝑐 𝑞 q-hypergeometric-rphis 2 1 𝑎 𝑏 𝑐 superscript 𝑞 𝑛 𝑞 𝑧 superscript 𝑞 𝑛 {\displaystyle{\displaystyle\mathcal{D}_{q}^{n}\left(\frac{\left(z;q\right)_{% \infty}}{\left(abz/c;q\right)_{\infty}}{{}_{2}\phi_{1}}\left({a,b\atop c};q,z% \right)\right)=\frac{\left(c/a,c/b;q\right)_{n}}{\left(c;q\right)_{n}(1-q)^{n}% }\left(\frac{ab}{c}\right)^{n}\frac{\left(zq^{n};q\right)_{\infty}}{\left(abz/% c;q\right)_{\infty}}{{}_{2}\phi_{1}}\left({a,b\atop cq^{n}};q,zq^{n}\right).}}
    0 references
    DLMF id
    DLMF:17.6.E26
    0 references
    Symbols used
    Q11298
    test
    ( a ; q ) n q-Pochhammer-symbol 𝑎 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}
    xml-id
    C17.S2.SS1.p1.m2ajdec
    0 references
     
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