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It has been recently realized (Rephaeli 1995) that the relativistic correctionsto the spectral distortions of the cosmic microwave background (CMB) measuredin the directions of galaxy clusters containing hot gas are significant and shouldbe detectable with the forthcoming experiments. In the present paper wecalculate the correction terms that are proportional to (V=c)n, with n = 2--4,and V r =c \Theta kT e =m e c2to the standard formulae describing the spectral distortionscaused...

Cosmic Microwave Background Radiation in the Direction of a Moving Cluster of Galaxies with Hot Gas: Relativistic Corrections