In mathematical analysis, **asymptotic analysis** is a method of describing limiting behavior. The methodology has applications across science. Examples are

- in computer science in the analysis of algorithms, considering the performance of algorithms when applied to very large input datasets
- the behavior of physical systems when they are very large.

The simplest example is, when considering a function *f*(*n*), there is a need to describe its properties when *n* becomes very large. Thus, if *f*(*n*) = *n*^{2}+3*n*, the term 3*n* becomes insignificant compared to *n*^{2} when *n* is very large. The function "*f*(*n*) is said to be asymptotically equivalent to *n*^{2} as *n* → ∞", and this is written symbolically as *f*(*n*) ~ *n*^{2}.

Reference: The Devil's Invention: Asymptotic, Superasymptotic and Hyperasymptotic Series (pdf)

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