Register to reply

Definition of asymptotic relation

by hanson
Tags: asymptotic, definition, relation
Share this thread:
hanson
#1
Jul19-06, 10:19 AM
P: 320
Hi all!

Can anyone explain to me why the asymptotic relation between a function and a power series is defined in such a way:

For all N,

[tex]
f(x) - \sum_{n=0}^N a_n(x-x_0)^n << (x-x_0)^N
[/tex]

How does this incorporate the idea of asymptoticity?

Please kindly help.
Phys.Org News Partner Mathematics news on Phys.org
Researcher figures out how sharks manage to act like math geniuses
Math journal puts Rauzy fractcal image on the cover
Heat distributions help researchers to understand curved space
arildno
#2
Jul19-06, 10:37 AM
Sci Advisor
HW Helper
PF Gold
P: 12,016
Quote Quote by hanson
Hi all!

Can anyone explain to me why the asymptotic relation between a function and a power series is defined in such a way:

For all N,

[tex]
f(x) - \sum_{n=0}^N a_n(x-x_0)^n << (x-x_{0})^{N}
[/tex]

How does this incorporate the idea of asymptoticity?

Please kindly help.
It means that:
[tex]\lim_{x\to{x}_{0}}\frac{f(x) - \sum_{n=0}^N a_n(x-x_0)^n}{(x-x_{0})^{N}}=0[/tex]


Register to reply

Related Discussions
Cartesian Product syntax in dictionary order relation definition Set Theory, Logic, Probability, Statistics 1
How is this asymptotic relation? Calculus & Beyond Homework 1
Asymptotic homework help Calculus 0
Asymptotic methods... Mechanical Engineering 0