2017-2018学年一湘《支西与积分换为潮路以一3 1.LeK2）=simz 22 (1)(6%)Show that 0 and are removable singularities. (2)(7%)Find the first three nonzero terms of the Taylor series around forz.What is the radius of convergence of this series (3)(7%)Set the Laurent series for sinz in the annulus<2 to be the following 品2以 then use the result of(2)to find the coefficients ccoc and c 8.()If f(z)is analytic in D.,and isunbounded in Dfor each integer n,then what kind of singularity does f(z)have at?Prove your conclusion. 2017-2018 学年第一学期《复变函数与积分变换》期终考试试卷--3 7. Let 2 2 1 1 2 ( ) sin z h z z z z  = − + − . (1) (6%) Show that 0 and  are removable singularities. (2) (7%) Find the first three nonzero terms of the Taylor series around 0 for h z( ) . What is the radius of convergence of this series. (3) (7%) Set the Laurent series for 1 sin z in the annulus     z 2 to be the following 1 = sin n n n c z z + =−  , then use the result of (2) to find the coefficients 2 1 0 1 c c c c , , , − − and 2 c .. 8. (10%) If f z( ) is analytic in D: 0 1   z , and ( ) n z f z is unbounded in D for each integer n, then what kind of singularity does f z( ) have at 0 ? Prove your conclusion