DLMF:17.2.E12 (Q5302)

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DLMF:17.2.E12
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    Statements

    Defining formula
    ( a ⁢ q - n ; q ) n ( b ⁢ q - n ; q ) n = ( q / a ; q ) n ( q / b ; q ) n ⁢ ( a b ) n . q-Pochhammer-symbol 𝑎 superscript 𝑞 𝑛 𝑞 𝑛 q-Pochhammer-symbol 𝑏 superscript 𝑞 𝑛 𝑞 𝑛 q-Pochhammer-symbol 𝑞 𝑎 𝑞 𝑛 q-Pochhammer-symbol 𝑞 𝑏 𝑞 𝑛 superscript 𝑎 𝑏 𝑛 {\displaystyle{\displaystyle\frac{\left(aq^{-n};q\right)_{n}}{\left(bq^{-n};q% \right)_{n}}=\frac{\left(q/a;q\right)_{n}}{\left(q/b;q\right)_{n}}\left(\frac{% a}{b}\right)^{n}.}}
    0 references
    DLMF id
    DLMF:17.2.E12
    0 references
    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.m2akdec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1kdec
    0 references
    Q11711
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1hdec
    0 references
     
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