Carsten Elsner

A universal functional equation

It is shown that the S-chains solving Rubels universal fourth-order differential equation also satisfy a third-order functional equation.

On a linear transcendence measure for the solutions of a universal differential equation at algebraic points

In this paper the author continues his work on arithmetic properties of the solutions of a universal differential equation at algebraic points. Every real continuous function on the real line can be uniformly approximated by C∞-solutions of a universal differential equation. An algebraic universal differential equation of order five and degree 11 is explicitly given, such that every finite set of nonvanishing derivatives y(k1)(τ),…,y(kr)(τ) (1⩽k1<⋯<kr) at an algebraic point τ is linearly independent over the field of algebraic numbers. A linear transcendence measure for these values is effectively computed.