We present the redshift evolutions and distributions of the gamma-ray luminosity and photon spectral index of flat spectrum radio quasar (FSRQ) type blazars, using non-parametric methods to obtain the evolutions and distributions directly from the data. The sample we use for analysis consists of almost all FSRQs observed with a greater than approximately 7 sigma detection threshold in the first year catalog of the Fermi Gamma-ray Space Telescopes Large Area Telescope, with redshfits as determined from optical spectroscopy by Shaw et al. We find that FSQRs undergo rapid gamma-ray luminosity evolution, but negligible photon index evolution, with redshift. With these evolutions accounted for we determine the density evolution and luminosity function of FSRQs, and calculate their total contribution to the extragalactic gamma-ray background radiation, resolved and unresolved, which is found to be 16(+10/-4)%, in agreement with previous studies.
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