# Complex number integration

1. May 31, 2008

I am stuck with a complex integration. Integrand looks like this:
Exp[-2*pi*i*(Rz+s*z)]. Integration is w.r.t z.
Where Rz is function of z, which is little complicated, but for simplicity we can assume z^3.
s is just other variable.
I was trying to do this integration in Mathematica. If I put Z instead of Z^3, then it runs otherwise it keeps running and never gives result.
Is there any other numerical integration method to perform this integration? I guess I can't do it in Simpson method, since this has complex number in it.
Any help is really appreciated.

Thanks
Veena

2. May 31, 2008

### foxjwill

Do you know contour integration?

3. May 31, 2008

### Dick

I think if you are going to pose an integration question you might want to specify the limits of the integration? If you want to integrate along a contour, what contour? If you want an antiderivative, what are R and S?

4. Jun 1, 2008

The limits of integration is 0 -> 4*pi. I guess it is not contour integration. There is no R. It is Rz, which is a function of z and S is another variable. after integration it will come in result.

Thanks
Vn

5. Jun 1, 2008

### Dick

Mathematica won't be able to produce an antiderivative for something like that. Yes, you can do it numerically. To integrate f(z)dz just split the integral up into real and imaginary parts. Then you can use Simpson's method on each of the parts. You could also use Simpson directly on the complex form - but it might be clearer this way.