Formula:6027

Digital Library of Mathematical Functions ID 17.2.E40

${\displaystyle{\displaystyle\sum_{j=0}^{2n}(-1)^{j}\genfrac{[}{]}{0.0pt}{}{2n}{j}_{q}=\left(q;q^{2}\right)_{n}.}}$

Symbols List

• ${\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle\genfrac{[}{]}{0.0pt}{}{\NVar{n}}{\NVar{m}}_{\NVar{q}}}}$: $$q$$ -binomial coefficient (or Gaussian polynomial)
• ${\displaystyle{\displaystyle q}}$: complex base
• ${\displaystyle{\displaystyle j}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
 

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