| Logarithmic-exponential series (2007) | |||||||||||||||||
Abstract | |||||||||||||||||
| Abstract. We extend the field of Laurent series over the reals in a canonical way to an ordered differential field of "LE-series " (logarithmic-exponential series), 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 operators to show that each LE-series has a formal integral. We give evidence 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-series and establish its basic properties, including the existence of compositional inverses. Various interesting subfields of the field of LEseries | |||||||||||||||||
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