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We present a detailed analysis of the two-point correlation function, from the 2dF Galaxy Redshift Survey (2dFGRS). We estimate the redshift-space correlation function, xi(s), from which we measure the redshift-space clustering length, s_0=6.82+/-0.28 Mpc/h. We also estimate the projected correlation function, Xi(sigma), and the real-space correlation function, xi(r), which can be fit by a power-law, with r_0=5.05+/-0.26Mpc/h, gamma_r=1.67+/-0.03. For r>20Mpc/h, xi drops below a power-law as is expected in the popular LCDM model. The ratio of amplitudes of the real and redshift-space correlation functions on scales of 8-30Mpc/h gives an estimate of the redshift-space distortion parameter beta. The quadrupole moment of xi on scales 30-40Mpc/h provides another estimate of beta. We also estimate the distribution function of pairwise peculiar velocities, f(v), including rigorously the effect of infall velocities, and find that it is well fit by an exponential. The accuracy of our xi measurement is sufficient to constrain a model, which simultaneously fits the shape and amplitude of xi(r) and the two redshift-space distortion effects parameterized by beta and velocity dispersion, a. We find beta=0.49+/-0.09 and a=506+/-52km/s, though the best fit values are strongly correlated. We measure the variation of the peculiar velocity dispersion with projected separation, a(sigma), and find that the shape is consistent with models and simulations. Using the constraints on bias from recent estimates, and taking account of redshift evolution, we conclude that beta(L=L*,z=0)=0.47+/-0.08, and that the present day matter density of the Universe is 0.3, consistent with other 2dFGRS estimates and independent analyses., 19 pages, revised following referee's report, and accepted by MNRAS. Higher resolution Figures, an animated version of Figure 12 and a colour version of Figure 22 are available from http://www.nottingham.ac.uk/~ppxeh/

We combine the 2MASS extended source catalogue and the 2dFGRS to produce an IR selected galaxy catalogue with 17,173 measured redshifts. We use this extensive dataset to estimate the J and K-band galaxy luminosity functions. The LFs are fairly well fit by Schechter functions with J: M*-5log h= -22.36+/-0.02, alpha= -0.93+/-0.04, Phi=0.0104+/-0.0016 h^3/Mpc^3 and K: M*-5log h= -23.44+/-0.03, alpha=-0.96+/-0.05, Phi=0.0108+/-0.0016 h^3/Mpc^3 (2MASS Kron magnitudes). These parameters assume a cosmological model with Omega=0.3 and Lambda=0.7. With datasets of this size, systematic rather than random errors are the dominant source of uncertainty in the determination of the LF. We carry out a careful investigation of possible systematic effects in our data. The surface brightness distribution of the sample shows no evidence that significant numbers of low surface brightness or compact galaxies are missed by the survey. We estimate the present-day distributions of B-K and J-K colours as a function of absolute magnitude and use models of the galaxy stellar populations, constrained by the observed optical and infrared colours, to infer the galaxy stellar mass function. Integrated over all galaxy masses, this yields a total mass fraction in stars (in units of the critical mass density) of Omega_*.h= (1.6+/-0.24)/10^3 for a Kennicutt IMF and Omega_*.h= (2.9+/-0.43)/10^3 for a Salpeter IMF. These values agree with those inferred from observational estimates of the star formation history of the universe provided that dust extinction corrections are modest., Typo in Table 3 Fixed (MNRAS 326 255). Catalogue with 17,173 2dFGRS z's at http://star-www.dur.ac.uk/~cole/2dFGRS-2MASS