也可以用公式求系数： f(z)=ln(1+z）=+a1z+a2z2+.+az+. ao f(0)=In1=i2nz 2"0 1 -1 =1 2:1+z)22=0 3= fn- 1 11×2×3 4:1+z)40 4 ·●●●●● 4=(-1011 In(1+z)=) 台k 2 k= 1 2 1 =Z- 231 4 ●●●●●● -7 2 十 3 0zk1) 232323 2 0 1 2 ( ) ln(1 ) . . k k f z z a a z a z a z = + = + + + + + 0 a f i n = = = (0) ln1 2  也可以用公式求系数： 1 0 1 1 '(0) 1, 1! 1 z a f z = = = = + 2 2 0 1 1 1 1 ''(0) , 2! 2! 2 (1 ) z a f z = − = = = − + ''' 3 3 0 1 1 2 1 (0) , 3! 3! 3 (1 ) z a f z = = = = + (4) 4 4 0 1 1 1 2 3 1 (0) 4! 4! (1 ) 4 z a f z =   = = = − + . 1 1 ( 1) , k k a k − = − . 1 1 1 2 3 4 , 2 3 4 = − + − +    z z z z 1 1 ( 1) ln(1 ) k k k z z k  − = − + =  (| | 1) z 