## C-R of Laurent Series

When doing complex contour integration one can use the C-R formula or the Laurent series and find the first coefficient of the priciple part. What are the selection criteria for choosing these methods?

Regards,

Hob
 PhysOrg.com science news on PhysOrg.com >> Ants and carnivorous plants conspire for mutualistic feeding>> Forecast for Titan: Wild weather could be ahead>> Researchers stitch defects into the world's thinnest semiconductor
 Recognitions: Gold Member Science Advisor Staff Emeritus What do you mean by "use the Cauchy-Riemann equations to do a contour integral"? Are you referring to actually integrating around the contour as opposed to summing the residues inside the contour?
 Hi, I mean summing within the contour. $$2 \pi$$ x $$\sum residues$$ = Integral around the contour. You can also use the Laurent Expansion and finding the first principle coefficient. I am unsure what method you would use when presented with a complex integration, Regards,

Recognitions:
Gold Member
??The "first principle coefficient" of the Laurent expansion, around pole $z_0$, by which I think you mean the coefficient of $z^{-1}$, is the residue at that $z_0$. They are the same method.