Rémi Jaoui: On the problem of integration in finite terms and exponentially algebraic functions

Abstract: Around 1835, Liouville introduced the class of elementary functions which are the holomorphic functions which can be constructed from the arithmetic operations, precomposition by the exponential and (branches of) the logarithm, and solutions of algebraic equations only. The problem of integration in finite terms asks to determine whether the solutions of a given differential equation are elementary functions or not and if they are to compute them effectively.

I will present an improvement on the classical results on this problem using the class of exponentially algebraic functions which is strictly larger than Liouville’s class of elementary functions. I will also describe some practical consequences of this improvement.

This is joint work with Jonathan Kirby.