Transcendental numbers and irrationality measure Is it possible to generate transcendental numbers of arbitrary irrationality measure ? I am thinking of something like an infinite series which depends on a parameter fixing the irrationality measure. 
All I have found so far is bounds on the irrationality measure of famous numbers, I have not been able to find something going the other way around.

Using one of the results at the Wolfram MathWorld web page for Irrationality Measure, it's fairly straightforward to construct simple continued fraction expansions that represent real numbers having any preassigned real number $m \geq 2$ as their irrationality measure.
In particular, see Jonathan Sondow's paper Irrationality Measures, Irrationality Bases, and a Theorem of Jarnik.
