Hardy notation
From Wikipedia, the free encyclopedia
In complexity theory and mathematics, the Hardy notation, introduced by G. H. Hardy, is used for asymptotic comparison of functions, equivalently to Landau notation (also known as "Big O notation").
It is defined in terms of Landau notation by
and 
(Similar symbols are used, like 
resp. 
.)
The Hardy notation is commonly abused similarly to the Landau notation. For example, where h2 = O(h3) is the shortened/abused Landau notation of 
, the expression 
is the shortened/abused Hardy notation of 
.
For more examples and applications, see Landau notation and references therein.
[edit] See also
- Big O notation: more explicit definitions, explanations, properties and related notations for real valued functions
- Taylor's theorem, maybe the most important application of Landau notation in mathematical analysis
- Asymptotic expansion: approximation of functions generalizing Taylor's formula.
- Nachbin's theorem: a precise way of bounding complex analytic functions so that the domain of convergence of integral transforms can be stated.
