A measurement of the form factors of charged kaon semileptonic decays is presented, based on 4.4 x 10(6)K(+/-) (0)e(e)(+/-) (Ke3 +/-) and 2.3 x 10(6)K(+/-) (0)+/- (K3 +/-) decays collected in 2004 by the NA48/2 experiment. The results are obtained with improved precision as compared to earlier measurements. The combination of measurements in the Ke3 +/- and K3 +/- modes is also presented.
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