DLMF:17.3.E8 (Q5348)

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DLMF:17.3.E8
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    Statements

    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
    DLMF id
    DLMF:17.3.E8
    0 references
    Symbols used
    Q10754
    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)
    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
     
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