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We use on-shell recursion relations to compute analytically the one-loopcorrections to maximally-helicity-violating n-gluon amplitudes in QCD. Thecut-containing parts have been computed previously; our work supplies theremaining rational parts for these amplitudes, which contain two gluons ofnegative helicity and the rest positive, in an arbitrary color ordering. Wealso present formulae specific to the six-gluon cases, with helicities (- + - ) and (- + + - + +), as well as numerical results for six, seven, and eightgluons. Our construction of the n-gluon amplitudes illustrates the relativelymodest growth in complexity of the on-shell-recursive calculation as the numberof external legs increases. These amplitudes add to the growing body ofone-loop amplitudes known for all n, which are useful for studies of generalproperties of amplitudes, including their twistor-space structure.Comment: 67 pages, 11 figures, v2 minor corrections, expanded discussion of numerical stabilit

All one-loop maximally helicity violating gluonic amplitudes in QCD