Question

please answer its urgent.

develop f(z)=(z(z-3)) into a laurent serkes valid for the following domains

7) 0 < 1 2 -3/ <3 6) 1८11-4/<4

develop g(z)= 1/((z-1)(z-2)) into a laurent series valid for the following domains

develop h(z)= z/((z+1)(z-2)) into a laurent series valid for the following domains

Answer 1

9 १(-) = 7(2-3) 7 domain ०/-3/ 23 f(z) is every where analytic Laurent series expension < (7-3) 22-37 8) domain ।</z-4/२५ here also f(?) is analytic. on t. = caurent series 72-37, D Z-2 (1) इना (22) g) domain .</2-1/<I (2) - (Z-1) (2-29 --- hauren series for (A-2) 1=1+² +22t- in 12lk1 न+ 11-2/</ च - (1+ (1-2)) [1 - (1-2) + (14-2)-- (1-3--] न -1 4 - 4-2 - . -1 Z-1 MH)1-7) - 120

Z-) 자2 ID) 0시2221시 (c) 굶 224 파리시 긽 (+19) ㅋ 2 - [1- (Z-2) + (z-2) -l2-294 - - ] 故 깨다29에 is the lawrent series of 912) in 0</2-229 2-2 - 2 베스 RE) > - 213 + 재 제 시 차2 ㅇ | 3 ㅋ ㅎ해 +름 제 글 채 랗 1렇시 릅 나떻게 FID - 「 + ' + +12 + 345 345)” m 6 // <3 यो ㅎ 제 g 3 + 32

h녀 래 = 2 +2 음 3 0 221~3 0< 시 해 +를 ㅢ ㅎ 첨가3 +3t를 긽 , t를 를 싫 1 시 내 끓릉긁 - + - --] + 글 층한 t5 (-1)() m 0시2213 - 2 M20