# Difficult integral

1. Feb 22, 2008

### Rednas

I fear that this one is really hard, if not impossible, but an analytic answer would be way more usefull than a numerical one. Who can help me in the right direction?

$\int_0^{arccos(a)} d\phi \frac{cos(\phi)}{(cos(\phi)+\sqrt{cos^2(\phi) - a^2})(x \sqrt{cos^2(\phi)-a^2}+y sin(\phi) + z + x_0 cos(\phi) )}$

with 0<a<1 and the phi integral only over positive values of the squareroot

Approximations for y=0 and a small are also welcome.

This integral comes from the double integral $\int_0^{\infty} dk\int_0^{2\pi}d\phi \frac{cos(\phi)}{(cos(\phi)+\sqrt{cos^2(\phi) - a^2}} e^{i k(x \sqrt{cos^2(\phi)-a^2}+y sin(\phi) + z + x_0 cos(\phi) )}$

Last edited: Feb 23, 2008
2. Feb 22, 2008

### Marco_84

i dont understan anything of what you wrote.
could you post somthing more readible...

use the buttons if you dont understand tex code.

ciao
marco

3. Feb 22, 2008

### sutupidmath

Yeah i agree with u! i am staring at it for a few minutes but it is quite hard to dechiper, quite ambiguous!

4. Feb 22, 2008

### Hurkyl

Staff Emeritus
Ambiguous? I don't think that word means what you think it means. :tongue: The expression is written in the syntax of Mathematica. (and I'm pretty sure it's syntactically correct)

5. Feb 22, 2008

### sutupidmath

Yeah i guess! I just wanted to say that it is hard to read what the OP posted, but i guess i said the wrong way!

6. Feb 25, 2008

### Rednas

Posted something more readable. Wasn't aware of the Tex possibilities at first, so I used the Mathematica syntax.

7. Feb 25, 2008

### sutupidmath

Let's hope someone will take the time to work this out, cuz it really looks nasty!!!

8. Jan 8, 2009