An approximation method and system for series expansion of functions include the steps and functions, respectively, of: expanding an input function in Taylor series up to an (N−1)-th term; expanding the input function in Taylor series up to the N-th term; multiplying the expanded result up to the (N−1)-th term by a predetermined weight α; combining the expanded result up to the (N−1)-th term, multiplied by α, and the expanded result up to the N-th term; and dividing the combined result by (α+1).