DLMF:17.6.E12 (Q5379)

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DLMF:17.6.E12
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    Statements

    test
    ( 1 - z ) ⁢ ϕ 1 2 ⁡ ( q , a ⁢ q b ⁢ q ; q , z ) = ∑ n = 0 ∞ ( a ⁢ q , a ⁢ z ⁢ q / b ; q ) n ( b ⁢ q , z ⁢ q ; q ) n ⁢ ( 1 - a ⁢ z ⁢ q 2 ⁢ n + 1 ) ⁢ ( b ⁢ z ) n ⁢ q n 2 , 1 𝑧 q-hypergeometric-rphis 2 1 𝑞 𝑎 𝑞 𝑏 𝑞 𝑞 𝑧 superscript subscript 𝑛 0 q-multiple-Pochhammer 𝑎 𝑞 𝑎 𝑧 𝑞 𝑏 𝑞 𝑛 q-multiple-Pochhammer 𝑏 𝑞 𝑧 𝑞 𝑞 𝑛 1 𝑎 𝑧 superscript 𝑞 2 𝑛 1 superscript 𝑏 𝑧 𝑛 superscript 𝑞 superscript 𝑛 2 {\displaystyle{\displaystyle(1-z){{}_{2}\phi_{1}}\left({q,aq\atop bq};q,z% \right)=\sum_{n=0}^{\infty}\frac{\left(aq,azq/b;q\right)_{n}}{\left(bq,zq;q% \right)_{n}}(1-azq^{2n+1})(bz)^{n}q^{n^{2}},}}
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    DLMF id
    DLMF:17.6.E12
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    constraint
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
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