q-derivative

Summary

The $q$-derivative of a function $f$ is the quotient $\frac{f(qx) - f(x)}{qx - x}$, where $q \ne 1$ is a fixed number. It replaces the limit in the ordinary derivative by a comparison of $f$ at $x$ and at the scaled point $qx$. It is the basic operator of $q$-calculus and of the theory of q-analogs, and it tends to the ordinary derivative as $q \to 1$. It is also called the Jackson derivative.