Tham khảo tài liệu 'advanced mathematical methods for scientists and engineers episode 2 part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | The series about z X for 1 z 2 is 1 _ 1 z 2 z 1 2 z 1 E -2 z . for 2 z 1 0 -1 2 z- -1 for z 2 0 _ 1 1 E 2 z for z 2 - To find the expansions in the three regions we just choose the appropriate series. 1. f z - ãh E -1 z - E y z for z 1 0 0 Ể -1 Í1 - V . for z 1 0 f z E -1 2 1 z for z 1 0 614 2. __f z r z - ĩ z__ 1 - n f z -1 n 1zn - Y y rzn. for 1 z 2 n X n 0 3. f . - 2 1 1 l n 1 -1 n 1zn - 2 zn. for 2 z 1 2n 1 1 f z 1 n 1 2 .zn. for 2 z n Solution Laurent Series. point z 0 of We assume that m is a non-negative integer and that n is an integer. The Laurent series about the m is f z E anzn n where an 1 1 fi dz i2n JC zn 1 .
