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We test the resummation techniques used in developing Pad\'e and EffectiveOne Body (EOB) waveforms for gravitational wave detection. Convergence testsshow that Pad\'e approximants of the gravitational wave energy flux do notaccelerate the convergence of the standard Taylor approximants even in the testmass limit, and there is no reason why Pad\'e transformations should help inestimating parameters better in data analysis. Moreover, adding a pole to theflux seems unnecessary in the construction of these Pad\'e-approximated fluxformulas. Pad\'e approximants may be useful in suggesting the form of fittingformulas. We compare a 15-orbit numerical waveform of the Caltech-Cornell groupto the suggested Pad\'e waveforms of Damour et al. in the equal mass,nonspinning quasi-circular case. The comparison suggests that the Pad\'ewaveforms do not agree better with the numerical waveform than the standardTaylor based waveforms. Based on this result, we design a simple EOB model bymodifiying the ET EOB model of Buonanno et al., using the Taylor series of theflux with an unknown parameter at the fourth post-Newtonian order that we fitfor. This simple EOB model generates a waveform having a phase difference ofonly 0.002 radians with the numerical waveform, much smaller than 0.04 radiansthe phase uncertainty in the numerical data itself. An EOB Hamiltonian can makeuse of a Pad\'e transformation in its construction, but this is the only placePad\'e transformations seem useful.

Ineffectiveness of Pad\'e resummation techniques in post-Newtonian approximations