- #1
- 2,704
- 19
Homework Statement
Sub problem from a much larger HW problem:
From previous steps we arrive at a complete elliptic integral of the second kind:
[tex]E(k)=\int_0^{\pi/2} dx \sqrt{1+k^2\sin^2x}[/tex]
In the next part of the problem, I need to expand this integral and approximate it by truncating at the first order term. (k is large)
Homework Equations
[tex]E(k) = \frac{\pi}{2} \sum_{n=0}^{\infty} \left[\frac{(2n)!}{2^{2 n} (n!)^2}\right]^2 \frac{k^{2n}}{1-2 n}[/tex]
The Attempt at a Solution
I believe I should use the expansion quoted above.
Here is my question. Based of the previous steps I know that k^2 has to be large. Also, the sign of k^2 is opposite of what is is in the standard form of E(k).
So, 1. Does this expansion truncated at first order approximate the integral well if k^2 is large?
I think not. Is there another expansion, one for large k^2, that I can potentially use?
2. Can I just change the sign in the odd terms of the expansion to account for the sign change of k?
I think this should work.