Logarithmic-exponential series

We extend the field of Laurent series over the reals in a canonical way to an ordered differential field of "logarithmic-exponential series" (LE-serie s), which is equipped with a well behaved exponentiation. We show that the LE-series with derivative 0 are exactly the real constants, and we invert o perators to show that each LE-series has a formal integral. We give evidenc e for the conjecture that the field of LE-series is a universal domain for ordered differential algebra in Hardy fields. We define composition of LE-s eries and establish its basic properties, including the existence of compos itional inverses. Various interesting subfields of the field of LE-series a re also considered. (C) 2001 Elsevier Science B.V. All rights reserved.