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If neutrinos have self-interactions, these will induce scatterings between astrophysical and cosmic neutrinos. Prior work proposed to look for possible resulting resonance features in astrophysical neutrino spectra in order to seek a neutrino self-interaction which can be either diagonal in the neutrino flavor space or couple different neutrino flavors. The calculation of the astrophysical spectra involves either a Monte Carlo simulation or a computationally intensive numerical integration of an integro-partial-differential equation. As a result only limited regions of the neutrino self-interaction parameter space have been explored, and only flavor-diagonal self-interactions have been considered. Here, we present a fully analytic form for the astrophysical neutrino spectra for arbitrary neutrino number and arbitrary self-coupling matrix that accurately obtains the resonance features in the observable neutrino spectra. The results can be applied to calculations of the diffuse supernova neutrino background and of the spectrum from high-energy astrophysical neutrino sources. We illustrate with a few examples.