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A theory for a quasi-one-dimensional incommensurate charge-density wave state arising from electron-phonon (el-phon) interaction connecting electron states in two different bands is presented. An expression for the fundamental component of the energy gap as a function of the effective el-phon coupling, valid for all coupling strengths, has been found. For a single band, the expression simplifies to a reciprocal hyperbolicsine dependence on the reciprocal effective coupling. The effectivedoi:10.1098/rspa.2010.0085 fatcat:iufj7iwv5vazlid7jmcfsgp43e