DLMF:17.2.E23 (Q5313)

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DLMF:17.2.E23
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    test
    ( q ⁢ a 1 k , q ⁢ ω k ⁢ a 1 k , … , q ⁢ ω k k - 1 ⁢ a 1 k ; q ) n ( a 1 k , ω k ⁢ a 1 k , … , ω k k - 1 ⁢ a 1 k ; q ) n = ( a ⁢ q k ; q k ) n ( a ; q k ) n = 1 - a ⁢ q k ⁢ n 1 - a , q-multiple-Pochhammer 𝑞 superscript 𝑎 1 𝑘 𝑞 subscript 𝜔 𝑘 superscript 𝑎 1 𝑘 … 𝑞 superscript subscript 𝜔 𝑘 𝑘 1 superscript 𝑎 1 𝑘 𝑞 𝑛 q-multiple-Pochhammer superscript 𝑎 1 𝑘 subscript 𝜔 𝑘 superscript 𝑎 1 𝑘 … superscript subscript 𝜔 𝑘 𝑘 1 superscript 𝑎 1 𝑘 𝑞 𝑛 q-Pochhammer-symbol 𝑎 superscript 𝑞 𝑘 superscript 𝑞 𝑘 𝑛 q-Pochhammer-symbol 𝑎 superscript 𝑞 𝑘 𝑛 1 𝑎 superscript 𝑞 𝑘 𝑛 1 𝑎 {\displaystyle{\displaystyle\frac{\left(qa^{\frac{1}{k}},q\omega_{k}a^{\frac{1% }{k}},\dots,q\omega_{k}^{k-1}a^{\frac{1}{k}};q\right)_{n}}{\left(a^{\frac{1}{k% }},\omega_{k}a^{\frac{1}{k}},\dots,\omega_{k}^{k-1}a^{\frac{1}{k}};q\right)_{n% }}=\frac{\left(aq^{k};q^{k}\right)_{n}}{\left(a;q^{k}\right)_{n}}=\frac{1-aq^{% kn}}{1-a},}}
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    DLMF id
    DLMF:17.2.E23
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