Little-O Notation

The symbol , pronounced "Little-O of ," is one of the Landau symbols and is used to symbolically express the asymptotic behavior of a given function.

In particular, if  is an integer variable which tends to infinity and  is a continuous variable tending to some limit, if  and  are positive functions, and if  and  are arbitrary functions, then it is said that provided that . Thus,  or  grows much faster than  or .

Note that Little-O notation is the inverse of Little-Omega notation, i.e., that

Additionally, Little-O notation is related to Big-O notation in that  is stronger than and implies .