Jackson integral

Summary

The Jackson integral, or $q$-integral, is a q-analog of the Riemann integral. It replaces the integral over $[0, a]$ by a weighted sum of the values of the function at the geometric sequence of points $a, aq, aq^2, \dots$. It is the inverse of the q-derivative in the same way as an integral is the inverse of a derivative. Many identities for basic hypergeometric series, such as $q$-beta integrals, are stated with it.