behavior. Transseries can also be convenient for representing functions. Through their inclusion of exponentiation and logarithms, transseries are a strong...

represented in floating-point. The field of transseries is larger than the Levi-Civita field. An example of a transseries is: e ln ⁡ ln ⁡ x + ln ⁡ ln ⁡ x + ∑...

Laboratoire d'informatique of the École Polytechnique. His research deals with transseries (i.e. generalizations of formal power series) with applications to algebraic...

1007/3-540-48686-0_21. ISBN 978-3-540-66200-6. MR 1730337. van der Hoeven, J. (2006). Transseries and Real Differential Algebra. Lecture Notes in Mathematics. Vol. 1888...

coefficients, where x is taken to be infinitesimal and positive the transseries real closed fields the superreal numbers the hyperreal numbers The surreal...

especially on asymptotic differential algebra and the model theory of transseries". In 2018, Aschenbrenner was an invited speaker at the International...

p-adic fields, valued fields, and finite fields, and to the study of transseries. With Alex Wilkie, he improved Gromov's theorem on groups of polynomial...

field T L E {\displaystyle \mathbb {T} ^{LE}} of logarithmic-exponential transseries. The field N o ( ε 0 ) {\displaystyle \mathbf {No} (\varepsilon _{0})}...

Boisgibault, his great grandson. Bendixson–Dulac theorem Hilbert's sixteenth problem Transseries Works by or about Henri Dulac at the Internet Archive...

(that contain Hardy L-functions as a subfield) can be defined using transseries. Every element of a Hardy field is eventually either strictly positive...

given coefficient c q {\displaystyle c_{q}} is finite. The field of transseries T {\displaystyle \mathbb {T} } is a directed union of Hahn fields (and...

Inst. Fourier, 42, 1992, 73-164 doi:10.5802/aif.1287 "Six Lectures on Transseries, Analytical Functions and the Constructive Proof of Dulac's Conjecture"...

ordered exponential field. The ordered field of logarithmic-exponential transseries T L E {\textstyle \mathbb {T} ^{LE}} is constructed specifically in a...