Asymptotic expansion

In calculus is an asymptotic result, a basic building block of an asymptotic analysis. The asymptotic result defines the approach an asymptotic expansion space and thus determines the possible results of the analysis.

Definition

A finite or infinite sequence of functions in the area called asymptotically when

With the Landau notation. For infinite sequences is called a uniform asymptotic sequence in n, if uniformly applicable in s, or from a uniform asymptotic result in the parameters, if the sequence depends on a parameter and applies uniformly in the parameters.

Examples

• The series of real functions.
• The sequence of real functions with for.

Properties

A partial sequence of an asymptotic sequence is also asymptotically, as well provides the potentiating the complete sequence with a positive number again an asymptotic result.