|
|
| View previous topic :: View next topic |
| Author |
Message |
Clearbluesky
Guest
|
 Posted: Sat May 26, 2007 11:01 am Post subject: Asymptotic Expansion of the Error Function |
 |
|
err(x) = sqrt(2/Pi) [int_0_x exp(-t^2 / 2) dt ]
| Quote: |
From this my notes go on to rewrite the integral between 0 and
infinity, to find an asymptotic expansion. Though the bit that throws |
me, is the fact that they get two different expansions which are valid
on two domains..(im not sure how the answer is obtained)
err(x) asymptotically equal to 1 - sqrt(2/Pi) exp(-x^2/2) Sum_k=0 to
infinity [(-1)^k (2k-1) !! /x^(2k+1)] as x--> infinity and the |arg x
| < 3Pi/4
it is also equal to (the |arg x| < Pi\4)
err(x) asymptotically equal to -1 - sqrt(2/Pi) exp(-x^2/2) Sum_k=0
to infinity [(-1)^k (2k-1) !! /x^(2k+1)] as x--> infinity and the |arg
x | < 3Pi/4
Note one has a minus one infront of it, the other doesn't.
Im not sure how the restrictions on the arg have been found?
any help would be much appreciated. |
|
| Back to top |
|
 |
| |
Ads |
Advertising
Sponsor
|
|
|
|
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum
|
|
FAQ
Search
Memberlist
Usergroups
Register
Profile
Log in to check your private messages
Log in
