DLMF:26.9.E7 (Q7880): Difference between revisions

From testwiki
Jump to navigation Jump to search
Newer edit →
imported>Admin
 
imported>Admin
Property / Symbols used
 
Property / Symbols used: $$q$$ -binomial coefficient (or Gaussian polynomial) / rank
 
Normal rank
Property / Symbols used: $$q$$ -binomial coefficient (or Gaussian polynomial) / qualifier
 
test:

[ n m ] q q-binomial 𝑛 𝑚 𝑞 {\displaystyle{\displaystyle\genfrac{[}{]}{0.0pt}{}{\NVar{n}}{\NVar{m}}_{\NVar% {q}}}}

\qbinom{\NVar{n}}{\NVar{m}}{\NVar{q}}
Property / Symbols used: $$q$$ -binomial coefficient (or Gaussian polynomial) / qualifier
 
xml-id: C17.S2.E27.m2acdec

Revision as of 13:58, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:26.9.E7
No description defined

    Statements

    test
    ∑ m , n = 0 ∞ p k ⁡ ( ≤ m , n ) ⁢ x k ⁢ q n = 1 + ∑ k = 1 ∞ [ m + k k ] q ⁢ x k = ∏ j = 0 m 1 1 - x ⁢ q j . superscript subscript 𝑚 𝑛 0 restricted-partitions-P-at-most 𝑘 absent 𝑚 𝑛 superscript 𝑥 𝑘 superscript 𝑞 𝑛 1 superscript subscript 𝑘 1 q-binomial 𝑚 𝑘 𝑘 𝑞 superscript 𝑥 𝑘 superscript subscript product 𝑗 0 𝑚 1 1 𝑥 superscript 𝑞 𝑗 {\displaystyle{\displaystyle\sum_{m,n=0}^{\infty}p_{k}\left(\leq m,n\right)x^{% k}q^{n}=1+\sum_{k=1}^{\infty}\genfrac{[}{]}{0.0pt}{}{m+k}{k}_{q}x^{k}=\prod_{j% =0}^{m}\frac{1}{1-x\,q^{j}}.}}
    0 references
    DLMF id
    DLMF:26.9.E7
    0 references
    Symbols used
    $$q$$ -binomial coefficient (or Gaussian polynomial)
    test
    [ n m ] q q-binomial 𝑛 𝑚 𝑞 {\displaystyle{\displaystyle\genfrac{[}{]}{0.0pt}{}{\NVar{n}}{\NVar{m}}_{\NVar% {q}}}}
    xml-id
    C17.S2.E27.m2acdec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q7880&oldid=44488"