Asymptotic behavior of coefficients


by intervoxel
Tags: asymptotic, behavior, coefficients
intervoxel
intervoxel is offline
#1
Feb3-11, 07:06 AM
P: 134
Given the difference equation

[tex]
a_{n+2}+A_n(\lambda)a_{n+1}+B_n(\lambda)a_n=0
[/tex]

where

[tex]
A_n(\lambda)=-\frac{(n+1)(2\delta+\epsilon+3(n+\gamma))+Q}{s(n+2)(n+1+\gamma)}
[/tex]

and

[tex]
B_n(\lambda)=\frac{(n+\alpha)(n+\beta)}{2(n+2)(n+1+\gamma)}
[/tex]

The asymptotic behavior of the coefficients is given by

[tex]
a_n^{(1)}\sim 2^{-n}n^{-1-\lambda/2}\sum_{s=0}^{\infty}\frac{c_s^{(1)}}{n^s}
[/tex]

and

[tex]
a_n^{(2)}\sim n^{-3}\sum_{s=0}^{\infty}\frac{c_s^{(2)}}{n^s}
[/tex]


I have to do the a similar calculation in my research project but I couldn't find out the procedure used. Please, someone can show me the steps to such a solution?

I tried to helplessly follow the text by Saber Elaydi, An Introduction to Difference Equations.
Phys.Org News Partner Science news on Phys.org
Simplicity is key to co-operative robots
Chemical vapor deposition used to grow atomic layer materials on top of each other
Earliest ancestor of land herbivores discovered

Register to reply

Related Discussions
Asymptotic Behavior of Solutions to Linear Equations Differential Equations 0
Asymptotic behavior of coefficients Differential Equations 2
Asymptotic behavior quadrupole potential Advanced Physics Homework 2
Asymptotic behavior and derivatives Calculus 1
asymptotic homework help Calculus 0