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Galaxy clustering data can be used to measure the cosmic expansion historyH(z), the angular-diameter distance D_A(z), and the linear redshift-spacedistortion parameter beta(z). Here we present a method for using effectivemultipoles of the galaxy two-point correlation function (\xi_0(s), \xi_2(s),\xi}_4(s), and \xi_6(s), with s denoting the comoving separation) to measureH(z), D_A(z)$, and beta(z), and validate it using LasDamas mock galaxycatalogs. Our definition of effective multipoles explicitly incorporates thediscreteness of measurements, and treats the measured correlation function andits theoretical model on the same footing. We find that for the mock data,\xi_0+\xi_2+\xi_4 captures nearly all the information, and gives significantlystronger constraints on H(z), D_A(z), and beta(z), compared to using only\xi_0+\xi_2.  We apply our method to the sample of luminous red galaxies (LRGs) from theSloan Digital Sky Survey (SDSS) Data Release 7 (DR7) without assuming a darkenergy model or a flat Universe. We find that \xi}_4(s) deviates on scales ofs<60Mpc/h from the measurement from mock data (in contrast to \xi_0(s),\xi_2(s), and \xi_6(s)), thus we only use \xi_0+\xi_2 for our fiducialconstraints. We obtain {H(0.35), D_A(0.35), Omega_mh^2, beta(z)} ={79.6_{-8.7}^{+8.3} km/s/Mpc, 1057_{-87}^{+88}Mpc, 0.103\pm0.015, 0.44\pm0.15}using \xi_0+\xi_2. We find that H(0.35)r_s(z_d)/c and D_A(0.35)/r_s(z_d) (wherer_s(z_d) is the sound horizon at the drag epoch) are more tightly constrained:{H(0.35)r_s(z_d)/c, D_A(0.35)/r_s(z_d)} = {0.0437_{-0.0043}^{+0.0041},6.48_{-0.43}^{+0.44}\} using \xi_0+\xi_2.

Using Multipoles of the Correlation Function to Measure H(z), D_A(z), and \beta(z) from Sloan Digital Sky Survey Luminous Red Galaxies