Deprecated: $wgMWOAuthSharedUserIDs=false is deprecated, set $wgMWOAuthSharedUserIDs=true, $wgMWOAuthSharedUserSource='local' instead [Called from MediaWiki\HookContainer\HookContainer::run in /var/www/html/w/includes/HookContainer/HookContainer.php at line 135] in /var/www/html/w/includes/Debug/MWDebug.php on line 372
DLMF:17.3.E8 - MaRDI portal

DLMF:17.3.E8 (Q6045)

From MaRDI portal





No description defined
Language Label Description Also known as
English
DLMF:17.3.E8
No description defined

    Statements

    DLMF defining formula
    A m , s ⁡ ( q ) = q ( s - m 2 ) + ( s 2 ) ⁢ ∑ j = 0 s ( - 1 ) j ⁢ q ( j 2 ) ⁢ [ m + 1 j ] q ⁢ ( 1 - q s - j ) m ( 1 - q ) m . q-Euler-number 𝑚 𝑠 𝑞 superscript 𝑞 binomial 𝑠 𝑚 2 binomial 𝑠 2 superscript subscript 𝑗 0 𝑠 superscript 1 𝑗 superscript 𝑞 binomial 𝑗 2 q-binomial 𝑚 1 𝑗 𝑞 superscript 1 superscript 𝑞 𝑠 𝑗 𝑚 superscript 1 𝑞 𝑚 {\displaystyle{\displaystyle A_{m,s}\left(q\right)=q^{\genfrac{(}{)}{0.0pt}{}{% s-m}{2}+\genfrac{(}{)}{0.0pt}{}{s}{2}}\sum_{j=0}^{s}(-1)^{j}q^{\genfrac{(}{)}{% 0.0pt}{}{j}{2}}\genfrac{[}{]}{0.0pt}{}{m+1}{j}_{q}\frac{(1-q^{s-j})^{m}}{(1-q)% ^{m}}.}}
    0 references
    Symbols used
    Q10728
    DLMF defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1abdec
    0 references
    $$q$$ -binomial coefficient (or Gaussian polynomial)
    DLMF defining formula
    [ n m ] q q-binomial 𝑛 𝑚 𝑞 {\displaystyle{\displaystyle\genfrac{[}{]}{0.0pt}{}{\NVar{n}}{\NVar{m}}_{\NVar% {q}}}}
    xml-id
    C17.S2.E27.m2adec
    0 references
    complex base
    DLMF defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1gdec
    0 references
    nonnegative integer
    DLMF defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C17.S1.XMD2.m1dec
    0 references
    nonnegative integer
    DLMF defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C17.S1.XMD3.m1dec
    0 references
    nonnegative integer
    DLMF defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C17.S1.XMD6.m1dec
    0 references

    Identifiers

     
    Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Item:Q6045&oldid=24174429"
    Powered by MediaWiki