Many years ago Friedman [3] determined those functions inSwhich have integral coefficients. Later authors extended this result to the case of functions with coefficients in an imaginary quadratic extension of the rationals [2, 4, 6]. In this paper these results are obtained in a significantly simpler manner and in addition there are found all functions in ∑ whose coefficients are half-integers in an imaginary quadratic extension of the rationals and with constant term zero in their Laurent expansions.