DLMF:17.6.E14 (Q5381)

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DLMF:17.6.E14
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    Statements

    test
    ∑ n = 0 ∞ ( a ; q ) n ⁢ ( b ; q 2 ) n ⁢ z n ( q ; q ) n ⁢ ( a ⁢ z ⁢ b ; q 2 ) n = ( a ⁢ z , b ⁢ z ; q 2 ) ∞ ( z , a ⁢ z ⁢ b ; q 2 ) ∞ ⁢ ϕ 1 2 ⁡ ( a , b b ⁢ z ; q 2 , z ⁢ q ) . superscript subscript 𝑛 0 q-Pochhammer-symbol 𝑎 𝑞 𝑛 q-Pochhammer-symbol 𝑏 superscript 𝑞 2 𝑛 superscript 𝑧 𝑛 q-Pochhammer-symbol 𝑞 𝑞 𝑛 q-Pochhammer-symbol 𝑎 𝑧 𝑏 superscript 𝑞 2 𝑛 q-multiple-Pochhammer 𝑎 𝑧 𝑏 𝑧 superscript 𝑞 2 q-multiple-Pochhammer 𝑧 𝑎 𝑧 𝑏 superscript 𝑞 2 q-hypergeometric-rphis 2 1 𝑎 𝑏 𝑏 𝑧 superscript 𝑞 2 𝑧 𝑞 {\displaystyle{\displaystyle\sum_{n=0}^{\infty}\frac{\left(a;q\right)_{n}\left% (b;q^{2}\right)_{n}z^{n}}{\left(q;q\right)_{n}\left(azb;q^{2}\right)_{n}}=% \frac{\left(az,bz;q^{2}\right)_{\infty}}{\left(z,azb;q^{2}\right)_{\infty}}{{}% _{2}\phi_{1}}\left({a,b\atop bz};q^{2},zq\right).}}
    0 references
    DLMF id
    DLMF:17.6.E14
    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.m2ahdec
    0 references
     
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