The imaginary-time Green’s function G(τ) in τ ∈ [0.4β, 0.6β] interval of the single-band half-filled Hubbard model. The Coulomb interaction strength U is 4.0 and β = 10. (a) G(τ) calculated by Legendre polynomials with or without integral kernel functions. (b) G(τ) calculated by Chebyshev polynomials with or without integral kernel functions. The maximum order for the polynomial expansion series, n_max, is 24. The ED data are used for comparison. All data are magnified by a factor of 100.