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Exact solution of QCD coupling constant

In Quantum chromodynamics, the quantum field theory of the Strong interaction, the coupling constant α s {\displaystyle \alpha _{\text{s}}} is computed perturbatively, the order n corresponding to Feynman diagrams including n quantum loops. The first order, n=1, solution is exact (at that order) and analytical. At higher orders, n>1, there is no exact and analytical solution and one typically uses an iterative method to furnish an approximate solution. However, for second order, n=2, the Lambert function provides an exact (if non-analytical) solution.