Section 8.1. Calculation of Residues: page 299la. 1.le. 1.le. 1.
lg. o.
li. e.lk. o.
lm. 4.
3a. ,,. 1 i"
3c. (1 - cos 1) 2 7ri.3e. i27r sinh 1.3g. 21r 3 i(^5) a. -2541ri.
7a. -"//'.
(^9) a. •+l l - z+2 l ·
9c. Z2 l -^2 ; + z +4^3.
9 0^2 I^2
· -;::} + (z- 1)2 - (z-1)" ·
ANSWERS 607ll. By T heorem 8.2 we have Res(g, n] = lim (z - n) g (z), wheren is any integer.
z -n
Since g(z) = 7rf (z)cot7rz = 7rf (z) ~~l;;l, and because/, is analytic at n,we use L'H6pit al's rule to get }~ si~C,;:J = 1. Explain how this gives the
result.Section 8.2. Trigonometric Integrals: page 3051.
,,.
2 ·
3.
,,.
2 ·
5.
,,.
4 ·7.^532 ,,..
9.
,,.
18.