DLMF:17.14.E1 (Q5470)

From DRMF
Revision as of 16:01, 29 December 2019 by Admin (talk | contribs) (‎Created a new Item: Wikidata Toolkit example test item creation)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:17.14.E1
No description defined

    Statements

    ( 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:17.14.E1
    0 references