  We report on an original and simple formulation of the phase shift in
N-light-pulse atom interferometers. We consider atomic interferometers based on
two-photon transitions (Raman transitions or Bragg pulses). Starting from the
exact analytical phase shift formula obtained from the atom optics ABCD
formalism, we use a power series expansion in time of the position of the
atomic wave packet with respect to the initial condition. The result of this
expansion leads to a formulation of the interferometer phase shift where the
leading coefficient in the phase terms up to T^k dependences (k >= 0) in the
time separation T between pulses, can be simply expressed in terms of a product
between a Vandermonde matrix, and a vector characterizing the two-photon pulse
sequence of the interferometer. This simple coefficient dependence of the phase
shift reflects very well the atom interferometer's sensitivity to a specific
inertial field in the presence of multiple gravito-inertial effects.
Consequently,we show that this formulation is well suited when looking for
selective atomic sensors of accelerations, rotations, or photon recoil only,
which can be obtained by simply zeroing some specific coefficients. We give a
theoritical application of our formulation to the photon recoil measurement.
