We combine the 2MASS extended source catalogue and the 2dF galaxy redshift survey to produce an infrared-selected galaxy catalogue with 17,173 measured redshifts .
We use this extensive dataset to estimate the galaxy luminosity functions in the J- and K _ { S } -bands .
The luminosity functions are fairly well fit by Schechter functions with parameters { M ^ { \star } _ { J } } -5 \log h = -22.36 \pm 0.02 , \alpha _ { J } = -0.93 \pm 0.04 , { \Phi ^ { \star } _ { J } } = 0.0104 \pm 0.0016 h ^ { 3 } Mpc ^ { -3 } in the J-band and { M ^ { \star } _ { K _ { S } } } -5 \log h = -23.44 \pm 0.03 , \alpha _ { K _ { S } } = -0.96 \pm 0.05 , { \Phi ^ { \star } _ { K _ { S } } } = 0.0108 \pm 0.0016 h ^ { 3 } Mpc ^ { -3 } in the K _ { S } -band ( 2MASS Kron magnitudes ) .
These parameters are derived assuming a cosmological model with \Omega _ { 0 } = 0.3 and \Lambda _ { 0 } = 0.7 .
With datasets of this size , systematic rather than random errors are the dominant source of uncertainty in the determination of the luminosity function .
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 _ { J } - K _ { S } and J - K _ { S } 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 _ { stars } h = ( 1.6 \pm 0.24 ) \times 10 ^ { -3 } for a Kennicutt IMF and \Omega _ { stars } h = ( 2.9 \pm 0.43 ) \times 10 ^ { -3 } for a Salpeter IMF .
These values are consistent with those inferred from observational estimates of the total star formation history of the universe provided that dust extinction corrections are modest .