# Asymptotic sequence

From Encyclopedia of Mathematics

A sequence of functions such that

where is a limit point of the set (finite or infinite). If the nature of is clear from the context, then one simply writes . If is an asymptotic sequence and is a function defined on , then will also be an asymptotic sequence.

Examples of asymptotic sequences:

1) ;

2) ;

3) ;

4) , where is an unbounded domain in the complex plane. Asymptotic sequences such as 1), 2) and 4) are called asymptotic power sequences.

#### Comments

#### References

[a1] | N.G. de Bruijn, "Asymptotic methods in analysis" , Dover, reprint (1981) |

[a2] | A. Erdélyi, "Asymptotic expansions" , Dover, reprint (1956) |

**How to Cite This Entry:**

Asymptotic sequence. M.I. Shabunin (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Asymptotic_sequence&oldid=11934

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098