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.  2003 Elsevier Science (USA). All rights reserved