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In this paper, I investigated the Doppler magnification effect in theflux-limited galaxy number counts with finite redshift bin width. Incontradiction with our intuition, the number counts correction formula fordifferent redshift bin are different. For the redshift window as delta functionand constant function, the correction formulas have been derived analyticallyin this paper. These two windows correspond to two extreme cases(i.e. extremelynarrow bin and extremely broad bin). An simulation have been implemented totest these formulas. The simulation results indicate the perturbation changessmoothly from one extreme case to another while extending the redshift binwidth from half bin width $0.05$ to $0.4$. As a result, Doppler magnificationcaused number counts perturbation of finite redshift bin width can NOT becompute via redshift integration of the perturbation formula derived with deltafunction redshift window. It is only a good approximation when the bin width issmall. These results are important for galaxy redshift survey kinematic dipoleestimation, and meaningful for the relativistic galaxy number counts angularpower spectrum estimation, such as CLASSgal and CAMB source.

Doppler magnification in flux-limited galaxy number counts with finite redshift bin width