Recent content by DanniHuang

If I turn everything into z-∏, do we need to use the same method as I used to work out z=0 and z=\frac{∏}{2}? But how? Turn the limit to z-∏→0? Because I used computer to work out the answer of z=∏ which is -1. But I still cannot get this answer by myself.

Homework Statement Find the residues of the function Homework Equations f(z)=\frac{1}{sin(z)} at z=0, \frac{∏}{2}, ∏ The Attempt at a Solution Since the function has a simple pole at z=0 I used: Res(f,0)=lim_{z->0}(z-0)\cdot\frac{1}{sin(z)}=1. This means the residue of the function at z=0...

Homework Statement To find the integral by Cauchy Residue Theorem and apply substitution method. Homework Equations To show: ∫^{2∏}_{0}\frac{cosθ}{13+12cosθ}=-\frac{4∏}{15} The Attempt at a Solution The solution I have done is attached. It is different as what the question wants me...

So n can only be even numbers with the Ʃa_{n}z^{n}=\frac{1}{n^{2}}. And then?

Homework Statement To find entire functions which satisfy g(\frac{1}{n}) = g(-\frac{1}{n}) = \frac{1}{n^{2}} Homework Equations How many functions can be found? The Attempt at a Solution Because the function is entire, it can be expanded in the Taylor series. But how can I work out the...

Homework Statement The question is needed to be done by using an appropriate substitution and the Cauchy Integral Formula. Homework Equations Evaluate the complex integral: ∫e^(e^it) dt, from 0 to 2∏ The Attempt at a Solution I cannot find an appropriate substitution for the integral.