Numerical Integration of a complex function with singularities

Hi all,

I've got a problem concerning the integration of the following function:

fun = @(s) (1-s.^2).^(1./2) .* (((1-s)/(1+s)).^(1i.*0.1103)) .* ((-1i.*(s./(sqrt(100.^2-s.^2))))./(u-s));

The integration limits are -b to b (given values). The variable "u" is used in a following integration with goes also from -b to b. For that following integration I created a for loop with lets u run in small steps from -b to b. After the for loop I use "trapz" to integrate the function. The problem is to find a solution for the first integral (function mentioned above). I tried quadgk and integral but I get always the warning:

Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 3.0e-06. The integral may not exist, or it may be difficult to approximate numerically. Increase MaxIntervalCount to 1514 to enable QUADGK to continue for another iteration.

Increasing the MaxIntervalCount doesnt help in this case. Has someone of you an idea?

Thank you all in advance!

[MatzeE]

Update: Cauchy Principal Value does also not help in this case...

[Torsten]

Did you plot Real(f), Imag(f) and abs(f) over [-b:b]^2 ?

Best wishes

Torsten.

[MatzeE]

Not jet. I tried it with surf(X,Y,Z) but not result so far ... Warning: Matrix is singular to working precision.

[MatzeE]

Update: The problem still exists

[Torsten]

What makes you think the integral exists ? I strongly doubt in it.

As you already noted, the function to be integrated has singularities at s=-1, s=+/- 100 and u=s ...

Best wishes

Torsten.