where the terms Ai (i = 1,2,3...) are given by the formula and where a can be positive, negative, fractional or whole. When the magnitude of z is less than 1, the higher powers get smaller and smaller and the formula can be made as precise as one wishes by including enough of them (for z of small magnitude, 1-2 terms are sufficient), although the result is never exact. For magnitudes of z equal to 1 or more, the formula only holds for values of a which are positive whole numbers. In that case, for any z, the result is exact and the sum of terms with powers of z does not go on arbitrarily but ends with z a.