Quantum dilogarithm

Summary

The quantum dilogarithm is a q-analog of the dilogarithm. In its basic form it is the infinite product $(x; q)_\infty = \prod_{n \ge 0} (1 - x q^n)$, whose logarithm is a deformed dilogarithm series. It satisfies a pentagon identity for $q$-commuting variables, a quantum version of the five-term relation. It appears in quantum groups, quantum Teichmüller theory, cluster algebras and knot invariants.