Abstract
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 ( k 1) ( τ),…, y ( k r ) ( τ) (1⩽ k 1<⋯< k r ) at an algebraic point τ is linearly independent over the field of algebraic numbers. A linear transcendence measure for these values is effectively computed.
Full Text
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call