  Time-delay interferometry is put forward to improve the signal-to-noise ratio
of space-borne gravitational wave detectors by canceling the large laser phase
noise with different combinations of measured data. Based on the Michelson data
combination, the sensitivity function of the detector can be obtained by
averaging the all-sky wave source positions. At present, there are two main
methods to encode gravitational wave signal into detector. One is to adapt
gravitational wave polarization angle depending on the arm orientation in the
gravitational wave frame, and the other is to divide the gravitational wave
signal into plus and cross polarizations in the detector frame. Although there
are some attempts using the first method to provide the analytical expression
of sensitivity function, only a semianalytical one could be obtained. Here,
starting with the second method, we demonstrate the equivalence of both
methods. First time to obtain the full analytical expression of sensitivity
function, which provides a fast and accurate mean to evaluate and compare the
performance of different space-borne detectors, such as LISA and TianQin.
