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1. ### Contour Integration

Eureka. Thanks a lot
2. ### Contour Integration

That clears up a lot in my foggy brain but there are still some issues. The y in the integral. Is this the complex part of the variable in the contour integral. i.e. z = x+iy. Or is it just some arbitrary variable. I thought that it was not connected to the integration variable in the contour...
3. ### Contour Integration

Homework Statement lim_{\alpha\rightarrow 0} \int_{-\infty}^{\infty} dx. e^{ixy}/(2\Pi i (x-i \alpha)) = H(y) where H(y) is the step function ie. H(y) = 1 for y > 0, H(y) = 0 (otherwise) Compute using an appropriate contour integral. Homework Equations -Laurent series -Residue...
4. ### Power series of a scalar function with a vector

I was trying to expand a scalar function with a power series but it accepts a vector argument. Do I simply use the multivariable power series expansion with the components of the vector acting as the argument OR do I use the single variable power series and take the vector's magnitude in the...