- Hardy notation
In
complexity theory andmathematics , the Hardy notation, introduced byG. H. Hardy , is used for asymptotic comparison of functions, equivalently toLandau 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 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.ee 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 boundingcomplex analytic functions so that the domain of convergence ofintegral transform s can be stated.
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