Questions tagged [q-analogs]

Use this tag for questions pretaining to q-analogs of functions, for example q-Binomials, $q$-derivatives, the q-theta function, the q-Pochhammer symbol, etc.

Use this tag for questions pertaining to $q$-analogs of functions, for example $q$-Binomials, $q$-derivatives, the $q$-theta function, the $q$-Pochhammer symbol, etc.

Read more about $q$-analogs in this Wikipedia article.

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A closed form of $q$-analog finite sum

Let $[n]:=\frac{1-q^n}{1-q}$. I wish to find a closed form of the following q-sum $$I(p):=\sum\limits_{n_1+\cdots+n_p=n\atop n_1,\ldots,n_p\ge 1}\ \ \ \frac{1}{[n_1]\cdots [n_p]}=?$$ For example, we have…
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