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Neutron stars (NSs) in low-mass X-ray binaries rotate at frequencies highenough to significantly deviate from sphericity ($\nu_* \sim$ 200--600 Hz). Weinvestigate the effects of rapid rotation on the observational appearance of aNS. We propose analytical formulae relating gravitational mass and equatorialradius of the rapidly rotating NS to the mass $M$ and radius $R$ of anon-rotating NS of the same baryonic mass using accurate fully relativisticcomputations. We compute spectra from an oblate rotating NS observed atdifferent inclination angles using the modified oblate Schwarzschild (MOS)approximation, where light bending is computed in Schwarzschild metric, butframe dragging and quadrupole moment of a NS are approximately accounted for inthe photon redshift calculations. We generalize the cooling tail method to thecase of a rapidly rotating NS to obtain the most probable values of $M$ and $R$of the corresponding non-rotating NS with the same baryonic mass. Weapproximate the local spectra from the NS surface by a diluted blackbody usingpreviously computed NS atmosphere models. We show that the NS radius could beoverestimated by 3--3.5 km for face-on stars of $R\approx 11$ km rotating at$\nu_* =$ 700 Hz if the version of the cooling tail method for a non-rotatingNS is used. We apply the method to an X-ray burst observed from the NS rotatingat $\nu_* \approx$ 532 Hz in SAX J1810.8$-$2609. The resulting radius of thenon-rotating NS (assuming $M=1.5 M_\odot$) becomes $11.8\pm0.5$ km if it isviewed at inclination i=60 deg and $R=11.2\pm0.5$ km for a face-on view, whichare smaller by 0.6 and 1.2 km than the radius obtained using standard coolingtail method ignoring rotation. The corresponding equatorial radii of theserapidly rotating NSs are 12.3$\pm 0.6$ km (for i=60 deg) and 11.6$\pm 0.6$\,km(for i=0 deg).

Observational appearance of rapidly rotating neutron stars: X-ray bursts, cooling tail method, and radius determination