A new computational framework for evaluation of the gamma function Γ(z) over complex plane is developed. The algorithm based on interpolation by rational functions, and generalizes classical methods Lanczos (SIAM J. Numer. Anal. B 1:86–96, (1964) Spouge Anal., 31(3):931–944, (1994) (which we show are also interpolatory). This utilizes exact poles function. By relaxing this condition allowing to...