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Preprints, Working Papers, ... Year : 2021

Hyperserial fields


Transseries provide a universal framework for the formal asymptotics of regular solutions to ordinary differential equations at infinity. More general functional equations such as E (x + 1) = exp E (x) may have solutions that grow faster than any iterated exponential and thereby faster than any transseries. In order to develop a truly universal framework for the asymptotics of regular univariate functions at infinity, we therefore need a generalization of transseries: hyperseries. Hyperexponentials and hyperlogarithms play a central role in such a program. The first non-trivial hyperexponential and hyperlogarithm are E and its functional inverse L, where E satisfies the above equation. Formally, such functions E and L can be introduced for any ordinal.
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hal-03196388 , version 1 (12-04-2021)


  • HAL Id : hal-03196388 , version 1


Vincent Bagayoko, Joris van der Hoeven, Elliot Kaplan. Hyperserial fields. 2021. ⟨hal-03196388⟩
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