Question

Complex Analysis:

Hi,
I have disagreement with answer from book:
Question:
Let G(z)= Integral of Contour of
elipse (x^2)/4 + (y^2)/9 = 1
of ((m^2 - m + 2)/(m - z))dm
Let's find G'(i) and G''(-i).

My Answer:
Set DU = (m^2 - m + 2);
Set DL = (m - z);
G'(z) = Integral of ((DU/ (DL^2))) dm
G''(z) = Integral of ((DU/ (DL^2)^2)) dm

According to the theorem 15 of section
4.5 of Fundamentals of Complex Analysis
(2 edition) of Dr. Saff and Dr. Snider

Once the integral is calculated by theorem 19, then the
G'(i) and G''(-i) is determined.
G'(i) = -4PI - 2(PI * i)
G''(-i) = (2/3) (PI * i)

Their solutions:
G'(z) = 2m - 1; G'(i) is same as mine
G''(z) = 2; And G''(-i) = 4 * PI * i; I think this is wrong

Can some one tell me which one is correct. Thx.

Where are you, KingGeorge? Thanks.

Thanks for all. But I found the answer, I am wrong due to the following:
G''(z) = Integral of ((DU/ (DL^2)^2)) dm;
It is supposed to be:
G''(z) = integral of ((DU/(DL^3))dm;
then the answer is 4*PI*i

Done deal. Thanks.