DLMF:17.2.E14 (Q5304)

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DLMF:17.2.E14
No description defined

    Statements

    Defining formula
    ( a ; q ) n - k ( b ; q ) n - k = ( a ; q ) n ( b ; q ) n ⁢ ( q 1 - n / b ; q ) k ( q 1 - n / a ; q ) k ⁢ ( b a ) k , q-Pochhammer-symbol 𝑎 𝑞 𝑛 𝑘 q-Pochhammer-symbol 𝑏 𝑞 𝑛 𝑘 q-Pochhammer-symbol 𝑎 𝑞 𝑛 q-Pochhammer-symbol 𝑏 𝑞 𝑛 q-Pochhammer-symbol superscript 𝑞 1 𝑛 𝑏 𝑞 𝑘 q-Pochhammer-symbol superscript 𝑞 1 𝑛 𝑎 𝑞 𝑘 superscript 𝑏 𝑎 𝑘 {\displaystyle{\displaystyle\frac{\left(a;q\right)_{n-k}}{\left(b;q\right)_{n-% k}}=\frac{\left(a;q\right)_{n}}{\left(b;q\right)_{n}}\frac{\left(q^{1-n}/b;q% \right)_{k}}{\left(q^{1-n}/a;q\right)_{k}}\left(\frac{b}{a}\right)^{k},}}
    0 references
    DLMF id
    DLMF:17.2.E14
    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.m2amdec
    0 references
    Q11715
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C17.S1.XMD1.m1adec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1mdec
    0 references
     
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