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:
4) , where is an unbounded domain in the complex plane. Asymptotic sequences such as 1), 2) and 4) are called asymptotic power sequences.
|[a1]||N.G. de Bruijn, "Asymptotic methods in analysis" , Dover, reprint (1981)|
|[a2]||A. Erdélyi, "Asymptotic expansions" , Dover, reprint (1956)|
Asymptotic sequence. M.I. Shabunin (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Asymptotic_sequence&oldid=11934