We study the production of the SM Higgs boson (H-0) at future e gamma colliders, through the reaction e gamma -->eH(0). The amplitude is evaluated using the non-linear R-xi-gauge, which greatly simplifies the calculation. Complete analytical expressions for the amplitudes are presented, which include the contributions from 1-loop triangles gamma gamma*H-0 and gamma Z*H-0 as well as the W- and Z-boxes with their related eeH(0) triangle graphs. The resulting cross section for this mechanism indicates that it could be used to detect the Higgs signal and to test its properties. (C) 1997 Published by Elsevier Science B.V.
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