Contour Integration

747
2
1. The problem statement, all variables and given/known data
Find the poles for the integrals:
[tex]
\int_{c}ds e^{st} \frac{1}{(s + \kappa + \frac{g^{2}}{s+\gamma+\gamma_{n}})}
[/tex]

One pole is at [tex] -(\gamma+\gamma_{n}) [/tex].

Is there another one?


Also
[tex]
\int_{c}ds e^{st} \frac{1}{(s + \kappa + \frac{g^{2}}{s+\gamma+\gamma_{n}})} \frac{1}{s+\gamma+\gamma_{n}} [/tex]
Similiarly, one pole is at [tex] -(\gamma+\gamma_{n}) [/tex].

Is there another one? I just need to be sure.

Thanks

2. Relevant equations



3. The attempt at a solution
 

Dick

Science Advisor
Homework Helper
26,249
611
Poles are the values of the integration variable s where the denominator vanishes, right? I don't think -(gamma+gamma_n) is a pole. In both cases, it looks to me like you are getting a relatively complicated quadratic in s.
 
747
2
Can you tell me what technique of integration I should use to evaluate this integral?

[tex]
\noindent\(\frac{e^{s t}}{g^2+(s+\text{yn}+\gamma ) (s+\kappa )}\)
[/tex]
 

Dick

Science Advisor
Homework Helper
26,249
611
The ordinary residue theorem, I think. You can write that as e^(st)/((s-p1)(s-p2)) where p1 and p2 are the poles you get from solving the quadratic equation. It's straightforward in principle, but I don't know a simple way to write the nasty expressions you get from solving the quadratic. Where are you getting these problems??
 

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