Asymptotic sequence
From Encyclopedia of Mathematics
A sequence of functions such that
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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. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Asymptotic_sequence&oldid=32993
Asymptotic sequence. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Asymptotic_sequence&oldid=32993
This article was adapted from an original article by M.I. Shabunin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article