  Large-angle fluctuations in the cosmic X-ray background are investigated by a
new formalism with a simple model of the X-ray sources. Our method is
formulated from the Boltzmann equation and a simple extension of the work by
Lahav et al. to be applicable to a hyperbolic (open) universe. The low
multipole fluctuations due to the source clustering are analyzed in various
cosmological models in both numerical and analytic way. The fluctuations
strongly depend on the X-ray sources evolution model, as pointed out
previously. It turns out that the nearby ($z \lesssim 0.1$) sources are the
dominant contributors to the large-angle fluctuations. If these nearby sources
are removed in an observed X-ray map, the dipole (low multipole) moment of the
fluctuation drastically decreases. In this case the Compton-Getting effect of
an observer's motion can be a dominant contribution to the dipole fluctuation.
This feature of fluctuation, relating to the matter power spectrum, is
discussed.
