q-analog

Summary

A q-analog of a formula or a theorem is a version with an extra parameter $q$, see the definition. It gives back the original in the limit $q \to 1$. The basic example is the q-integer $[n]_q = 1 + q + \cdots + q^{n-1}$, which tends to $n$. From it one builds q-factorials, Gaussian binomial coefficients and q-series. Good q-analogs often have a meaning of their own, such as counts over finite fields or generating functions of statistics on permutations.