Fractional power approximation and its generation

For an analog simulating system, an approximating system is proposed. Its mathematical form is expressed by an algebraic equation: ƒ (x) ≈ α + β χ + γχk with four parameters given by real numbers. Their values can be determined so as to satisfy a best fit in a Chebyshev sense. Then, the accuracy is of the same order with that obtained by any kind of ordinary power series up to terms o f the third order. It is noticeable that a given function can be accurately approximated by this equation without destroying its uniform continuity.