# Extensions by Antiderivatives, Exponentials of Integrals and by Iterated Logarithms - Mathematics > Classical Analysis and ODEs

Extensions by Antiderivatives, Exponentials of Integrals and by Iterated Logarithms - Mathematics > Classical Analysis and ODEs - Download this document for free, or read online. Document in PDF available to download.

Abstract: Let F be a characteristic zero differential field with an algebraicallyclosed field of constants, E be a no-new-constant extension of F byantiderivatives of F and let y1,

., yn be antiderivatives of E. Theantiderivatives y1,

., yn of E are called J-I-E antiderivatives if thederivatives of yi in E satisfies certain conditions. We will discuss a newproof for the Kolchin-Ostrowski theorem and generalize this theorem for a towerof extensions by J-I-E antiderivatives and use this generalized version of thetheorem to classify the finitely differentially generated subfields of thistower. In the process, we will show that the J-I-E antiderivatives arealgebraically independent over the ground differential field. An example of aJ-I-E tower is extensions by iterated logarithms. We will discuss the normalityof extensions by iterated logarithms and produce an algorithm to compute itsfinitely differentially generated subfields.

Author: ** V. Ravi Srinivasan**

Source: https://arxiv.org/