Fock scattering functions are necessarily used in the solution of curved surface diffraction problems faced by terrestrial communication system designers. These functions must be interpolated when their arguments are between -3 and 2. In the conventional method, a two-point Lagrange formula is used for interpolation, and 51 complex coefficients are needed. In this study, it is shown that Fock scattering functions can be evaluated by using the minimum property of Chebyshev polynomials. In this approach, only 20 complex coefficients are enough. This method is found to be less memory demanding, less time consuming, and consequently more efficient than Lagrange interpolation.