Light but massive cosmological neutrinos do not cluster significantly on small scales, due to their high thermal velocities. With finite masses, cosmological neutrinos become part of the total matter field and contribute to its smoothing. Structure formation in the presence of massive neutrinos is therefore impeded compared to that in the standard $Lambda$CDM cosmology with massless neutrinos. Neutrinos masses also distort the anisotropy power spectrum of cosmic microwave background (CMB). Furthermore, a finite chemical potential $mu$ for cosmological neutrinos, still allowed by current data, would have a non-negligible impact on CMB and structure formation. We consistently evaluate effects of neutrino masses and chemical potentials on the matter power spectrum by use of a neutrino-involved N-body simulation, with cosmological parameters obtained from a Markov-Chian Moonte-Carlo (MCMC) refitting of CMB data. Our results show that while a finite averaged neutrino mass $m_ u$ tends to suppress the matter power spectrum in a range of wave numbers, the neutrino degeneracy parameters ${xi_i equiv mu_i /T}$ ($i=$1, 2, 3) enhance the latter, leading to a large parameter degeneracy between $m_ u$ and $xi_i$. We provide an empirical formula for the effects on the matter power spectrum in a selected range of wave numbers induced by $m_ u$ and $eta equiv sqrt{sum_i xi^2_i}$. Observing a strong correlation between $m_ u$ and $eta$, we propose a single redshift-independent parameter $m_ u - frac{4}{3}eta^2$ to characterize the neutrino effects on the matter power spectrum.
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