DLMF:17.6.E10 (Q5377)

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DLMF:17.6.E10
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    Statements

    Defining formula
    ( 1 - z ) ⁢ ϕ 1 2 ⁡ ( q , a ⁢ q b ⁢ q ; q , z ) = ∑ n = 0 ∞ ( b / a ; q ) n ⁢ ( - a ⁢ z ) n ⁢ q ( n 2 + n ) / 2 ( b ⁢ q , z ⁢ q ; q ) n , 1 𝑧 q-hypergeometric-rphis 2 1 𝑞 𝑎 𝑞 𝑏 𝑞 𝑞 𝑧 superscript subscript 𝑛 0 q-Pochhammer-symbol 𝑏 𝑎 𝑞 𝑛 superscript 𝑎 𝑧 𝑛 superscript 𝑞 superscript 𝑛 2 𝑛 2 q-multiple-Pochhammer 𝑏 𝑞 𝑧 𝑞 𝑞 𝑛 {\displaystyle{\displaystyle(1-z){{}_{2}\phi_{1}}\left({q,aq\atop bq};q,z% \right)=\sum_{n=0}^{\infty}\frac{\left(b/a;q\right)_{n}(-az)^{n}q^{(n^{2}+n)/2% }}{\left(bq,zq;q\right)_{n}},}}
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    DLMF id
    DLMF:17.6.E10
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    constraint
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
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    Symbols used
    Q11298
    Defining formula
    ( 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.m2afdec
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