  We compute spectral function for $^4$He by combining coupled-cluster theory
with an expansion of integral transforms into Chebyshev polynomials. Our method
allows to estimate the uncertainty of spectral reconstruction. The properties
of the Chebyshev polynomials make the procedure numerically stable and
considerably lower in memory usage than the typically employed Lanczos
algorithm. We benchmark our predictions with other calculations in the
literature and with electron scattering data in the quasi-elastic peak. The
spectral function formalism allows one to extend ab-initio lepton-nucleus cross
sections into the relativistic regime. This makes it a promising tool for
modeling this process at higher energy transfers. The results we present open
the door for studies of heavier nuclei, important for the neutrino oscillation
programs.
