Formula:6021

Digital Library of Mathematical Functions ID 17.2.E34

${\displaystyle{\displaystyle\lim_{n\to\infty}\genfrac{[}{]}{0.0pt}{}{rn+u}{sn+t}_{q}=\frac{1}{\left(q;q\right)_{\infty}}=\prod_{j=1}^{\infty}\frac{1}{(1-q^{j})},}}$

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
• ${\displaystyle{\displaystyle r}}$: nonnegative integer
• ${\displaystyle{\displaystyle s}}$: nonnegative integer
 

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