  We study the impact of the use of the power series expression for the
primordial tensor spectrum on parameter estimation from future direct detection
gravitational wave experiments. The spectrum approximated by the power series
expansion may give large deviation from the true (fiducial) value when it is
normalized at CMB scale because of the large separation between CMB and direct
detection scales. We derive the coefficients of the higher order terms of the
expansion up to the sixth order within the framework of the slow-roll
approximation and investigate how well the inclusion of higher order terms
improves the analytic prediction of the spectrum amplitude by comparing with
numerical results. Using the power series expression, we consider future
constraints on inflationary parameters expected from direct detection
experiments of the inflationary gravitational wave background and show that the
truncation of the higher order terms can lead to incorrect evaluation of the
parameters. We present two example models; a quadratic chaotic inflation model
and mixed inflaton and curvaton model with a quartic inflaton potential.
