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We compute the quadrupole mode of the gravitational waveform of inspirallingcompact binaries at the third and a half post-Newtonian (3.5PN) approximationof general relativity. The computation is performed using the multipolarpost-Newtonian formalism, and restricted to binaries without spins moving onquasi-circular orbits. The new inputs mainly include the 3.5PN terms in themass quadrupole moment of the source, and the control of required subdominantcorrections to the contributions of hereditary integrals (tails and non-linearmemory effect). The result is given in the form of the quadrupolar mode (2,2)in a spin-weighted spherical harmonic decomposition of the waveform, and may beused for comparison with the counterpart quantity computed in numericalrelativity. It is a step towards the computation of the full 3.5PN waveform,whose knowledge is expected to reduce the errors on the location parameters ofthe source.

The third and a half post-Newtonian gravitational wave quadrupole mode for quasi-circular inspiralling compact binaries