I am not familar with this theorem.
Consider a contour in a semicircular fashion with . So we get,
Now you need to find the poles and their residues and add them up to get your result.
I have another question for you that I'm stuck on. I get an answer on ipi*e^(ipi/6) can anyone confirm this?
Heres the question:
Note that theorem 1.1 is as follows:
Let p and q be polynomial functions such that:
1. the degree of q exceeds the degree of p by at least 2
2. any poles of p/q on the non-negative real axis are simple
Then for 0<a<1,
Integral (p(t)/q(t))t^a dt = -(pie^-piai cosec pia)S - (picot(pia)T
Where S is the sum of the residues of the function
f1(z) = p(z)/q(z) exp(alog2pi(z))
in C2pi and T is the residues of the function
f2(z)=p(z)/q(z) exp (alogz)
on the positive real axis