Formula:6020

Digital Library of Mathematical Functions ID 17.2.E33

${\displaystyle{\displaystyle\lim_{n\to\infty}\genfrac{[}{]}{0.0pt}{}{n}{m}_{q}=\frac{1}{\left(q;q\right)_{m}}=\frac{1}{(1-q)(1-q^{2})\cdots(1-q^{m})},}}$

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
• ${\displaystyle{\displaystyle m}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
 

Resources that cite this formula

No records found.