The question

Evaluate the following integral using Cauchy Integral Formula,

My attempt

Not analytic at:

This is inside the contour, so we use CIF as follows:

However, the solution is

Where have I gone wrong? Thanks.

Printable View

- Jun 16th 2011, 02:55 AMGlitchCauchy Integral Formula
**The question**

Evaluate the following integral using Cauchy Integral Formula,

**My attempt**

Not analytic at:

This is inside the contour, so we use CIF as follows:

However, the solution is

Where have I gone wrong? Thanks. - Jun 16th 2011, 03:23 AMchisigmaRe: Cauchy Integral Formula
... may be that the reason is that in the function has a pole with multeplicity two... in that case the formula for the residue is different respect to the case of a pole with multeplicity one...

Kind regards

- Jun 16th 2011, 04:00 AMGlitchRe: Cauchy Integral Formula
Ahh, I just discovered the generalised CIF equation.

Still not sure how to get the correct solution though, I did:

=

Not sure where the divide by 9 is coming from. :/ - Jun 16th 2011, 09:00 AMchisigmaRe: Cauchy Integral Formula
For a pole of order n is...

(1)

In our case is...

(2)

... so that...

(3)

... and for any closed path c containing the point is...

(4)

Kind regards

- Jun 16th 2011, 09:40 AMGlitchRe: Cauchy Integral Formula
Ahh, I just had to pull the 3 out of the denominator.

Thanks.