Little o notation
From Citizendium, the Citizens' Compendium
The little o notation is a mathematical notation which indicates that the decay (respectively, growth) rate of a certain function or sequence is faster (respectively, slower) than that of another function or sequence. It is often used in particular applications in physics, computer science, engineering and other applied sciences.
More formally, if f and g are real valued functions of the real numbers then the notation 
indicates that for every real number 
there exists a positive real number 
(note the dependence of T on 
) such that 
for all 
When the function g does not vanish this may be rewritten simply as
Similarly, if 
and 
are two numerical sequences then 
means that for any 
and n big enough one has 
(in case when is not zero, this means the limit of the fraction 
vanishes in the limit).
The little o notation is also often used to indicate that the absolute value of a real valued function goes to zero around some point at a rate faster than at which the absolute value of another function goes to zero at the same point. For example, suppose that f is a function with 
for some real number 
. Then the notation 
, where g(t) is a function which is continuous at t=0 and with g(0)=0, denotes that for every real number there exists a neighbourhood 
of such that 
holds on .
