This paper presents simple analytic approximations to the linear power spectra, linear growth rates, and rms mass fluctuations for both components in a family of cold + hot dark matter (CDM+HDM) models that are of current cosmological interest. The formulas are valid for a wide range of wave numbers, neutrino fractions, redshifts, and Hubble constants: k ≲ 10 h Mpc −1 , 0.05 ≲ Ω v ≲ 0.3, 0 ≤ z ≤ 15, and 0.5 ≤ h ≤ 0.8. A new, redshift-dependent shape parameter, Γ v = a 1/2 Ω v h 2 , is introduced to simplify the multidimensional parameter space and to characterize the effect of massive neutrinos on the power spectrum. The physical origin of Γ v lies in the neutrino free-streaming process, and the analytic approximations can be simplified to depend only on this variable and Ω v . Linear calculations with these power spectra as input are performed to compare the predictions of Ω v ≲ 0.3 models with observational constraints from the reconstructed linear power spectrum and cluster abundance. The usual assumption of an exact scale-invariant primordial power spectrum is relaxed to allow a spectral index of 0.8 ≲ n ≤ 1. It is found that a slight tilt of n = 0.9 (no tensor mode) or n = 0.95 (with tensor mode) in Ω v ~ 0.1–0.2 CDM + HDM models gives a power spectrum similar to that of an open CDM model with a shape parameter Γ = 0.25, providing good agreement with the power spectrum reconstructed by Peacock & Dodds and the observed cluster abundance at low redshifts. Late galaxy formation at high redshifts, however, will be a more severe problem in tilted models.
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