DLMF:17.3.E8 (Q5348)

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DLMF:17.3.E8
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    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}}.}}
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    DLMF:17.3.E8
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