DLMF:17.14.E1 (Q5470): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11711 / rank
 
Normal rank
Property / Symbols used: Q11711 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11711 / qualifier
 
xml-id: C17.S1.XMD4.m1dec
Property / Symbols used
 
Property / Symbols used: Q11719 / rank
 
Normal rank
Property / Symbols used: Q11719 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11719 / qualifier
 
xml-id: C17.S1.XMD8.m1dec

Latest revision as of 15:11, 2 January 2020

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DLMF:17.14.E1
No description defined

    Statements

    Defining formula
    ( q ; q ) a 1 + a 2 + ⋯ + a n ( q ; q ) a 1 ⁢ ( q ; q ) a 2 ⁢ ⋯ ⁢ ( q ; q ) a n =  coeff. of  ⁢ x 1 0 ⁢ x 2 0 ⁢ ⋯ ⁢ x n 0 ⁢  in  ⁢ ∏ 1 ≤ j < k ≤ n ( x j x k ; q ) a j ⁢ ( q ⁢ x k x j ; q ) a k . q-Pochhammer-symbol 𝑞 𝑞 subscript 𝑎 1 subscript 𝑎 2 ⋯ subscript 𝑎 𝑛 q-Pochhammer-symbol 𝑞 𝑞 subscript 𝑎 1 q-Pochhammer-symbol 𝑞 𝑞 subscript 𝑎 2 ⋯ q-Pochhammer-symbol 𝑞 𝑞 subscript 𝑎 𝑛  coeff. of  superscript subscript 𝑥 1 0 superscript subscript 𝑥 2 0 ⋯ superscript subscript 𝑥 𝑛 0  in  subscript product 1 𝑗 𝑘 𝑛 q-Pochhammer-symbol subscript 𝑥 𝑗 subscript 𝑥 𝑘 𝑞 subscript 𝑎 𝑗 q-Pochhammer-symbol 𝑞 subscript 𝑥 𝑘 subscript 𝑥 𝑗 𝑞 subscript 𝑎 𝑘 {\displaystyle{\displaystyle\frac{\left(q;q\right)_{a_{1}+a_{2}+\cdots+a_{n}}}% {\left(q;q\right)_{a_{1}}\left(q;q\right)_{a_{2}}\cdots\left(q;q\right)_{a_{n}% }}=\mbox{ coeff. of }x_{1}^{0}x_{2}^{0}\cdots x_{n}^{0}\mbox{ in }\prod_{1\leq j% <k\leq n}\left(\frac{x_{j}}{x_{k}};q\right)_{a_{j}}\left(\frac{qx_{k}}{x_{j}};% q\right)_{a_{k}}.}}
    0 references
    DLMF id
    DLMF:17.14.E1
    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.m2adec
    0 references
    Q11715
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C17.S1.XMD1.m1dec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1dec
    0 references
    Q11712
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C17.S1.XMD2.m1dec
    0 references
    Q11711
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1dec
    0 references
    Q11719
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C17.S1.XMD8.m1dec
    0 references
     
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