On the zeros of Flett's function

摘要

A constructive semilocal existence theorem for the function F: C→C F(x)≔∑k=1∞1ksinxk, called Flett's function is given. The constructive part of the theorem consists of an efficient numerical procedure to compute the zeros of F; its efficiency is based on special properties of F. For the real zeros a way is shown how to find starting approximations. It is illustrated by an example that the error estimate obtained is very sharp.