Formula:8572

Digital Library of Mathematical Functions ID 26.9.E6

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \sum_{n=0}^{\infty}\nrestpartitions[k]@{\leq m}{n}q^{n}=\qbinom{m+k}{k}{q}.}

Symbols List

• ${\displaystyle{\displaystyle\genfrac{[}{]}{0.0pt}{}{\NVar{n}}{\NVar{m}}_{\NVar{q}}}}$: $$q$$ -binomial coefficient (or Gaussian polynomial)
• ${\displaystyle{\displaystyle p_{\NVar{k}}\left(\leq\NVar{m},\NVar{n}\right)}}$:
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle m}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle q}}$: parameter
 

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